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ELEMENTARY 


LESSONS    IN     PHYSICS 


MECHANICS  {INCLUDING  HYDROSTATICS) 
AND  LIGHT 


BY 

EDWIN  H.  HALL,  Ph.D. 

Atsistant  Pro/essor  oy  Physics  in  Harvard  College 


NEW  YORK 
HENRY   HOLT   AND   COMPANY 

1894 


Copyright,  1894 

BY 

Henry  Holt  &  Co. 


FOBERT   DRUMMONP,   ELECTROTVPER  AND   PRINTER,    NEW  YORK. 


INTRODUCTION. 


Some  years  ago  a  body  of  educational  leaders  declared 
themselves  in  favor  of  teaching  physics  by  means  of  ex- 
periments involving  exact  measurement  and  weighing  by 
the  pupils  in  grammar-schools.  To  the  author  of  this 
book,  well  aware  of  the  difficulty  of  establishing  and  main- 
taining a  thorough  course  of  quantitative  experimental 
work  in  academies  and  high  schools,  the  new  proposition 
did  not  at  first  commend  itself.  Difficulties  of  various 
kinds,  financial,  mechanical,  pedagogical,  appeared  in  the 
way.  Indeed,  the  author  at  first  expressed,  somewhat 
publicly,  the  opinion  that  grammar-school  pliysics  must 
be  lecture-table  physics,  an  hour  or  two  a  week  devoted  by 
the  teacher  to  the  performance  and  discussion  of  simple 
experiments  in  the  presence  of  the  pupils.  He  thought, 
and  still  thinks,  that  such  a  course  would  be  not  unprofit- 
able. There  are  several  books  describing  this  kind  of 
work,  and  their  number  is  rapidly  increasing. 

But  the  advocates  of  the  lecture-table  method  of  science- 
teaching  cannot  claim  for  it  the  disciplinary  advantage 
and  the  power  of  bringing  the  pupil  into  close  quarters 
with  physical  facts  and  laws,  that  belong  to  a  properly- 
conducted  course  of  laboratory  work  by  the  pupils  them- 
selves. If  such  a  laboratory  course  is  readily  practicable, 
grammar-school  pupils  should  have  it,  for  the  grammar- 

Ui 

2066130 


iv  INTRODUCTION. 

school  is  the  popular  school,  the  school  in  which  the  great 
majority  of  children  get  the  last  of  their  formal  education. 
To  what  extent,  then,  is  quantitative  laboratory  work  in 
physics  practicable  for  grammar-schools  ?  The  question 
is  here  limited  to  quantitative  work,  because  the  author 
would  shrink  from  the  task  of  laying  out  a  course  not 
mainly  quantitative,  which  would  occupy  the  pupils  profit- 
ably without  making  impossible  demands  upon  the  time 
and  patience  of  the  teacher. 

Quantitative  work  of  a  substantial  and  profitable  char- 
acter is,  in  the  opinion  of  the  author,  practicable  for  gram- 
mar-school pupils  in  the  subjects  of  mechanics  (inchiding 
hydrostatics)  and  light.  Quantitative  work  in  sound,  heat, 
electricity,  and  magnetism  demands  apparatus  and  labora- 
tory facilities  that  school-boards  would  at  present  hesitate 
to  supply  to  grammar-schools,  even  if  it  were  certain  that 
pupils  of  fourteen  years  could  use  them  to  advantage. 

This  little  book  has  grown  out  of  a  course  of  instruction 
given  by  the  author,  for  two  years  in  succession,  to  teach- 
ers conducting,  or  preparing  to  conduct,  a  similar  course 
in  the  grammar-schools  of  Cambridge.  A  large  part  of 
the  work  for  pupils  described  in  this  book  has  been  actu- 
ally performed  by  whole  classes  in  the  highest  grade  of  all 
these  schools  during  the  year  1893-94.  The  success  of 
this  *'  Cambridge  experiment "  has  been,  on  the  whole, 
gratifying.  A  brief  account  of  the  way  in  which  this  new 
work  has  been  fitted  into  the  school  program  is  given,  in 
an  appendix  to  this  book,  by  Mr.  Frederick  S.  Cutter,  who 
was  the  first  grammar-school  master  in  Cambridge  to 
undertake  laboratory  teaching  in  physics. 

It  is  the  firm  conviction  of  the  author  that  class  labora- 
tory work  not  accompanied  by  persistent,  energetic,  teach- 
ing is  sure  to  be  a  failure.  We  are  often  told  that  the 
favorite  method  of  the  elder  Agassiz  with  a  new  pupil  was 
to  set  him  to  gaze  in  solitude  at  a  single  fish  for  two  or 


introduction:  v 

three  days.  Those  who  would  make  this  tlie  model  for 
science-teaching  in  general  forget  that  j3ure  observation  of 
numerous,  minute,  varied  details  plays  a  much  more  im- 
portant part  in  natural  history  than  in  physics.  The 
teacher  of  physics  who  would  produce  good  and  lasting 
results  must  see  to  it  not  merely  that  the  laboratory  work 
shall  be  carefully  done,  but  that  the  proper  lessons  shall 
be  drawn  from  it  and  the  proper  applications  made.  In 
fact,  the  young  pupil  should  give  as  much  time  to  the 
study  of  physics  in  the  lecture-  or  recitation-room  as  in 
the  laboratory  proper.  The  Suggestions  for  the  Lecture- 
room  given  in  this  book  are  sometimes  very  full,  but  in 
general  they  will  have  to  be  supplemented  by  hints  from 
other  books  or  from  the  teacher's  own  experience.  One 
or  two  text-books  of  the  high-school  grade,  and  if  possible 
some  book  of  the  college  grade.  Barker,  Deschanel,  or 
Ganot,  for  instance,  should  be  at  the  service  of  the  teacher. 

The  laboratory  Exercises  of  this  course  cover  about  one 
third  of  the  ground  covered  by  the  laboratory  Exercises  of 
Hall  and  Bergen's  Text-book  of  Physics,  and  most  of 
them  are  in  close  correspondence  with  the  work  in  physics 
recommended  by  the  Report  of  the  famous  "Committee 
of  Ten."  It  is  the  hope  of  the  author  that  the  use  of  this 
book  in  the  last  year  of  the  Grammar  School,  or  the  first 
year  of  the  High  School,  course  will  remove  much  of  the 
difficulty  now  found  by  some  schools  in  condensing  all  of 
the  laboratory  work  in  physics  into  one  year  of  the  High 
School.  The  discontinuity  thus  introduced  into  the  study 
of  physics,  a  break  of  two  or  three  years  between  the  study 
of  mechanics  and  optics,  on  the  one  hand,  and  heat, 
sound,  and  electricity  and  magnetism  on  the  other,  is  en- 
tirely reasonable,  in  view  of  the  much  greater  expense  and 
experimental  difficulty  of  laboratory  work  in  these  latter 
subjects. 

The  course  is  intended  to  run  through  the  year  and  to 


vi  INTRODUCTTON. 

occupy  the  pupil  two  school -periods,  each  forty  minutes 
long  if  possible,  per  week;  one  usually  in  the  laboratory, 
and  the  other  in  the  lecture-  or  recitation-room.  The 
number  of  Exercises  is  only  twenty-seven,  much  less  than 
the  number  of  school-weeks  in  the  year,  but  some  of  them 
may  prove  to  be  too  long  for  a  single  school-period,  and 
teachers  will  welcome  an  occasional  opportunity  for  repe- 
tition or  review.  The  Cambridge  Grammar-schools  have 
given  only  one  school-period  per  week  to  the  laboratory 
work,  and  have,  therefore,  not  been  able  to  do  all  the 
Exercises  in  one  year. 

Although  much  of  whatever  is  new  in  this  book  has 
originated  with  the  author,  many  valuable  suggestions  have 
come  to  him  from  teachers  and  from  makers  of  apparatus. 
Perhaps  the  most  striking  innovation  of  the  book  is  a 
method  of  measuring  the  index  of  refraction  of  liquids  by 
means  of  an  extremely  simple  and  inexpensive  apparatus 
which  yields  very  satisfactory  results. 

The  book  follows,  as  a  rule,  the  method  of  leading  up  to 
the  statement  of  laws  by  means  of  carefully-chosen  experi- 
ments, rather  than  the  opposite  one  of  giving  experiments 
as  illustrations  or  proofs  of  laws  already  stated.  It  can 
hardly  be  said  for  the  former  method  that  it  teaches  the  art 
of  making  discoveries, — that  art  is  as  difficult  to  teach  as 
the  art  of  getting  rich, — but  it  has  a  tendency  to  keep  the 
pupil  in  a  more  active,  self-dependent  state  of  mind  than 
the  latter  method,  and  in  particular  it  prevents  in  a  large 
measure  that  state  of  bias,  or  preconception,  in  the  perform- 
ance of  experiments,  which  is  so  dangerous  not  merely  to 
accuracy  of  observation  but  to  mental  rectitude.  On  the 
other  hand,  the  teacher  using  the  method  of  this  book  must 
not  allow  his  pupils  to  think  that  their  experiments,  even 
when  most  satisfactory,  really  demonstrate  the  rigid  accu- 
racy of  any  7iumerical  law, — the  law  of  a  balanced  lever,  for 
instance.    He  should  ask  of  them,  "What  law  do  your  ex- 


INTRODUCTION.  Vll 

periments  indicate  as  true?"  and  after  their  answer  he 
should  tell  them  whether  their  inference  is  or  is  not  in 
accordance  with  the  opinion  held  by  those  best  qualified 
to  judge  of  the  matter  in  question. 

Realizing  that  this  book  will  naturally  be  used  by  teach- 
ers little  accustomed  to  physical  manipulations  or  the  con- 
struction of  physical  apparatus,  the  author  has  taken 
especial  pains  in  the  description  of  laboratory  operations, 
and  has  endeavored  to  give,  in  Appendix  A,  complete,  de- 
tailed, lists  of  all  those  articles  used  in  the  laboratory  exer- 
cises and  the  lecture-room  experiments,  which  are  not  easily 
procurable  by  the  teacher.  A  number  of  firms,  mentioned 
by  name  in  that  Appendix,  have  undertaken  to  supply  the 
apparatus  described  in  these  lists  at  reasonable  prices.  A 
table  like  those  used  in  the  Cambridge  Grammar-schools  is 
described  in  the  same  Appendix.  Thus  the  mechanical 
difficulties  of  undertaking  the  course  described  in  this  book 
are  reduced  to  a  minimum. 

In  the  Cambridge  Grammar-schools  the  classes,  whatever 
their  size,  have  usually  been  divided  into  sections  of  sixteen 
or  less  for  laboratory  work,  and  as  only  one  section  in  a 
school  has  worked  in  the  laboratory  at  one  time,  only  six- 
teen sets  of  the  pupils'  apparatus  have  been  supplied  to  each 
school.  These  sixteen  sets  can  now  be  furnished  for  about 
$80.00  or  $90.00.  The  laboratory  for  a  section  of  sixteen 
requires  two  substantial  tables,  which  may  cost  $45.00  or 
$50.00.  The  teacher's  list  of  apparatus  and  certain  mis- 
cellaneous supplies  will  cost  about  $30.00.  Much,  and  if 
necessary  all,  of  the  pupils'  apparatus  can  be  on  shelves 
under  the  laboratory  tables.  Making  no  allowance  for 
apparatus-cases,  and  assuming  the  school-building  to  have 
an  available  room  fifteen  feet  by  twenty,  or  larger,  well 
lighted  and  supplied  with  a  cold-water  tap  and  a  sink,  one 
may  estimate  the  cost  of  establishing  this  course  fully  in 
any  grammar-school  at  $200.00,  a  considerable  margin  of 


Vlll  INTRODUCTION. 

this  estimate  being  intended  to  cover  contingencies  not  j 

specifically  foreseen.  ' 

Whatever  the  merits  or  demerits  of  the  course  laid  dov^^n  ' 

in  this  book,  its  success  in  any  particular  case  will  depend  ' 

largely  upon  local  conditions.     The  author  can  ask  for  it  ; 

no  more  favorable  trial  than  the  good-will  of  the  school  \ 

authorities  and  the  zeal  and  ability  of  the  teachers  have  \ 

given  it  at  Cambridge.  j 


TITLES  OF  THE  LABORATORY  EXERCISES. 


CHAPTER  I. 

MEASUREMENT  OF  DISTANCE,  AREA,  AND  VOLUME. 

PAGE 

1.  Measurement  of  a  Straight  Line 2 

2.  Lines  of  the  Right  Triangle  and  the  Circle 4 

3.  Area  op  an  Oblique  Parallelogram 7 

4.  Area  of  Plane  Triangles  7 

5.  Volume  of  a  Rectangular  Body  by  Displacement  of 

Water 10 

-    CHAPTER  II. 

DENSITY  AND  SPECIFIC  GRAVITY:    FLUID  PRESSURE. 

6.  Weight  of  Unit  Volume  op  a  Substance 13 

7.  Lifting    Effect    op   Water    upon  a  Body  Entirely 

Immersed  in  it 15 

8.  Weight  of  Water  Displaced  by  a  Floating  Body...     18 

9.  Ratio  between  the  Weight  of  a  Solid  Body  and  the 

Weight  op  an  Equal  Bulk  op  Water 23 

10.  Specific  Gravity  of  a  Block  of  Wood  by  Use  op  a 

Sinker 26 

11.  Specific  Gravity  by  Flotation  Method 29 

12.  Specific  Gravity  of  a  Liquid  :  Two  Methods 32 

CHAPTER  III. 

THE  LEVER. 

13.  The  Straight  Lever '. 36 

14.  Centre  of  Gravity  and  Weight  op  a  Lever 41 

ix 


X         TITLES  OF  THE  LABORATORY  EXERCISES. 

PAGE 

15.  Levers  of  the  Second  and  Third  Classes 45 

16.  Force  Exerted  at  the  Fulcrum  of  a  Lever 47 

CHAPTER  IV. 

THREE  FORCES  WORKING  THROUGH  ONE  POINT. 

17.  Three    Forces  in  One  Plane  and  All  Applied  to 

One  Point 53 

CHAPTER  V. 

FRICTION. 

18.  Friction  between  Solid  Bodies 63 

CHAPTER  VL 
THE  PENDULUM. 

CHAPTER  VII. 

LIGHT:  REFLECTION. 

19.  Images  in  a  Plane  Mirror 72 

20.  Combination  of  Two  Plane  MiitKORS :   Kaleidoscope.  78 

21.  Images  Formed  by  a  Convex  Cylindrical  Mirror 79 

22.  Concave  Cylindrical  Mirror 83 

CHAPTER  VIII. 

LIGHT:  REFRACTION. 

23.  Index  of  Refraction  from  Air  to  Water S8 

24.  Focal  Length  of  a  Lens 93 

25.  Relation  of  Image-distance  to  Object-distance  ;  Con- 

jugate Foci  of  a  Lens 95 

26.  Shape  and  Size  of  a  Real  Image  Formed  by  a  Lens.     98 

27.  Virtual  Image  Formed  by  a  Lens 100 


PHYSICAL  EXPERIMENTS. 


CHAPTEE  I. 


MEASUREMENT   OF  DISTANCE,  AREA,  AND   VOLUME. 


Suggestion  for  the  Teacher  as  to  Preparation  for 
Exercise  1. 

The  line  to  be  measured  may  be  along  the  edge  of  a 
table  (or  sheet  of  paper)  from  one  fine  scratch  to  another, 
a  distance  of  about  15  inches.  It  is  a  great  convenience  to 
have  all  the  pupils  measure  equal  distances;  accordingly, 
the  teacher  is  advised  to  lay  off  these  distances  by  some 
method  like  the  following :  A  carpen- 
ter's square  is  placed  along  the  edge 
of  the  table  as  in  Fig.  1,  and  while  it 
is  held  firmly  in  place  a  fine  light 
scratch  is  made  with  the  point  of  a 
sharp  knife-blade  at  right  angles  with 
the  edge  of  the  table  at  the  points  a  and  5.  The  distance 
from  a  to  J  is  the  one  to  be  measured  by  the  pupil.  The 
first-described  method  of  using  the  measuring-stick  in  the 
following  Exercise  is  not  a  good  method,  but  it  is  one  that 
many  will  use  if  they  are  not  properly  instructed.  The 
second  method  is  a  good  one,  and  the  two  are  here  brought 
together  in  order  that  the  pupil  may  see  at  once  the  right 
way  and  the  wrong  way  to  use  such  an  instrument. 


Fig.  1. 


2  PHYSICAL  EXPERIMENTS. 

Much  of  the  interest  and  profit  of  the  Exercise  will 
come  from  the  opportunity  given  each  pupil  to  compare 
his  own  work  with  that  of  others. 

Any  piece  of  apparatus  to  be  used  in  theExercises  will 
usually  be  referred  to  by  the  number  it  bears  in  the  list  of 
apparatus  given  at  the  end  of  the  book. 

EXERCISE    1. 

MEASUREMENT  OF  A  STRAIGHT  LIKE. 

Apparatus:  A  short  measuring-stick  (No.  1)  and  a  meter-rod 
(No.  2). 

To  each  pupil  is  given  a  measuring-stick  about  one-fourth  as 
long  as  the  distance  from  a  to  b.  We  -will  suppose  that  these 
sticks  are  made  by  sawing  a  meter-rod,  graduated  to  millimeters, 
into  ten  equal  parts.  The  saw-cut  will  usually  leave  the  divis- 
ions at  the  very  ends  of  the  sticks  imperfect,  and  these  divisions 
should  not  be  used  in  the  measurements. 

Xiet  each  pupil  measure  his  distance  at  least  t\7ice  carefully, 
with  his  measuring-stick  laid  flat  upon  the  table,  the  marks  upon 
the  stick  being  thus  horizontal,  and  let  him  write  upon  the  black- 
board the  results  of  his  two  measurements. 

Then  let  each  pupil  measure  his  distance  twice  again,  this  time 
placing  his  measuring-stick  upon  its  edge,  so  that  the  marks  upon 
it  Avill  be  vertical,  making  a  light,  fine  mark  upon  the  table  with  a 
sharp  pencil  to  set  the  stick  by,  whenever  it  is  moved  forward  a 
length.  These  new  measurements  are  also  to  be  placed  upon  the 
blackboard  under  the  first  ones. 

Finally  let  each  pupil  measure  his  w^hole  distance  at  once  with 
his  meter-rod  and  write  this  last  measurement  vrith  the  others. 

To  judge  of  the  accuracy  of  a  set  of  measurements  it  is 
not  enough  to  know  how  much  these  differ  among  them- 
selves, for  the  importance  of  the  difference  usually  depends 
upon  the  ratio  which  the  difference  bears  to  the  whole 
quantity  measured.  A  thousandth  part  of  an  inch  might 
be  a  very  serious  difference  to  a  watchmaker  in  the  meas- 
urement of  some  small  cylinder,  while  a  difference  of  sev- 
eral inches  in  the   measurement  from  one   mile-post  to 


MEASUREMENT  OF  DISTANCE,  AREA,  VOLUME.      3 

another  would  be  of  but  little  consequence.  The  pupil 
should  therefore  form  the  habit  of  comparing  his  errors, 
or  the  differences  of  his  measurements,  with  the  whole 
quantity  that  he  had  to  measure. 

Let  us  suppose,  for  instance,  that  in  this  Exercise  the 
measurements  made  by  one  pupil  are  37.30  cm.,  37.00  cm., 
and  37.10  cm.  The  greatest  difference  is  found  between 
the  first  and  second.  It  is  0.3  cm.,  and  its  ratio  to  37.15 
cm.,  which  is  midway  between  37.30  cm.  and  37.00  cm.,  is 
0.0081.  We  see,  then,  that  the  difference  between  the  two 
measurements  of  the  line  is  about  eight  one-thousandths, 
not  quite  one  per  cent,  of  the  length  of  the  line. 

Each  pupil  should  make  a  similar  calculation  from  his 
own  measurements  in  Exercise  1. 

Suggestions  for  the  Lecture-room. 

The  importance  of  having  definite  units  of  length,  of 
weight,  etc.,  so  that  any  man  in  dealing  with  his  neighbor 
may  know  just  how  much  is  meant  by  the  words  foot, 
pound,  and  the  like,  is  so  great  that  in  all  civilized  coun- 
tries the  exact  meaning  of  such  words  is  fixed  by  law,  and 
very  great  care  is  taken  to  make  and  preserve  government 
standards,  as  they  are  called,  standard  yard-sticks,  stand- 
ard pound- weights,  for  instance,  with  which  as  patterns 
the  measuring  instruments  used  in  business  are  compared 
and  tested. 

Interesting  accounts  of  the  foot,  the  yard,  the  meter, 
etc.,  can  be  found  in  almost  any  encyclopedia. 

Meter-rods  for  school  use  are  in  many  cases  marked  oflf 
in  inches  on  one  side.  With  the  information  given  by 
such  a  rod  the  class  can  find  how  many  centimeters  are 
equal  to  one  inch.  This  number  carried  to  two  places  of 
decimals  is  accurate  enough  for  most  purposes. 


4  PHYSICAL  EXPERIMENTS. 

EXERCISE   2. 

THE  LINES  OF  THE  BIGHT  TRIANGLE  AND  THE  CIRCLE. 

Appsuratus :  A  30-cm.  measuring-stick  (No.  3).  A  sheet  of  paper 
upon  which  is  drawn  carefully  a  right  triangle  no  side  of  which 
is  less  than  10  cm.  long.  (No  two  pupils  should  use  exactly  similar 
triangles.)  A  cylinder  of  wood  4  or  5  cm.  in  diameter  (No.  4).  A 
narrow  straight-edged  strip  of  thin  paper. 

Part  l. — IVIeasurement  of  the  Sides  of  a  Right  Triangle. 
— Let  each  pupil  measure  very  carefully  all  the  sides  of  his 
triangle,  not  being  content  to  read  to  the  nearest  0.1  cm-,  but 
striving  to  note  and  measure  0.05  cm.  distances,  if  he  can  do  so 
•without  hurting  his  eyes. 

After  the  measiurements  are  made  square  the  length  of  each 
side  and  compare  the  greatest  square  with  the  sum  of  the  other 
two  squares.  The  conclusion  drawn  from  this  comparison  must 
not  be  extended  to  triangles  which  are  not  right-angled. 

Part  2. — Measurement  of  the  Circumference  and  Diam- 
eter OF  a  Circle. — Measure  carefully  the  diameter  of  one 
end  of  the  cylinder.  Then  wrap  the  strip  of  paper  around  the 
curved  surface  of  the  cylinder  at  the  same  end,  and  mark  upon 
the  edge  of  the  strip  the  point  where  the  second  winding  of  the 
paper  begins  to  overlap  the  first.  Then  unfold  the  paper  and 
measure  upon  it  that  distance  which  extended  once  around  the 
cylinder.  Then  divide  this  distance,  w^hich  of  course  is  equal  to 
the  circumference  of  the  circle,  by  the  length  of  the  diameter. 
The  ratio  thus  obtained  is  one  w^hich  it  is  important  to  know, 
although  w^e  shall  not  have  much  occasion  to  use  it  in  this  book. 
Mathematicians,  physicists,  and  engineers  use  it  so  much  that  they 
have  a  particular  sign,  7t,  to  denote  it. 

This  sign  is  a  Greek  letter  and  is  called  pe  by  students  of  Greek, 
but  when  used  as  just  described  it  is  often  called  pie  to  distinguish 
it  from  p. 

Suggestions  for  the  Lecture-room. 

The  measurements  of  Exercise  2  may  be  discussed  some- 
what as  follows:  The  square  of  the  longest  side  of  the 
triangle  is  found  by  one  pupil  to  be  404.01  and  the  sum  of 
the  squares  of  the  other  two  sides"  406,05,    If  the  two 


MEASUREMENT  OF  DISTANCE,  AREA,   VOLUME.      5 

f  short  sides  were  measured  correctly,  how  large  an  error  in 
the  measurement  of  the  longest  side  would  cause  the  dis- 
agreement here  found  ?  The  long  side  was  measured  as 
20.10  cm.  If  it  had  been  called  20.20  cm.,  its  square 
would  have  been  408.04,  which  is  about  as  much  too  large 
as  the  square  actually  found  is  too  small.  If  the  distance 
had  been  measured  as  20.15  cm.,  the  square  would  have 
been  406.02,  a  quantity  very  close  indeed  to  the  sum  of 
the  other  two  squares.  If,  therefore,  the  original  error  lay 
entirely  in  the  measurement  of  the  longest  side,  this  error 
must  have  been  very  nearly  0.05  cm.  Of  course  the  error 
may  have  been  made  in  measuring  the  other  sides,  or  in 
drawing  the  triangle,  or  in  all  parts  of  the  work.  An 
error  which  mistakes  20.15  for  20.10,  or  201.5  for  201.0,  or 
2015  for  2010,  is  called  in  each  case  an  error  of  5  parts  in 
2015,  or  1  part  in  403,  or  an  error  of  about  ^  per  cent  (see 
remarks  following  Exercise  1). 

Question  for  the  Class. 

In  the  case  of  the  circle,  which  would  make  the  greater 
difference  in  the  result  (circumference  -^  diameter),  an 
error  of  0.05  cm.  in  the  measurement  of  the  diameter  or 
an  error  of  0.10  cmo  in  the  measurement  of  the  circum- 
ference ? 

Surface. 

Thus  far  we  have  been  measuring  the  length  of  lines. 
To  measure  a  line,  as  we  see,  is  merely  to  find  out  by  trial 
that  it  is  so  many  centimeters  or  inches  long.  A  line  10. 6 
cm.  long  is  one  that  could  be  divided  into  ten  full  centi- 
meters and  six  tenths  of  another  centimeter.  We  here 
call  the  centimeter  our  unit  of  length. 

If  we  have  to  measure  a  surface,  the  whole  table-top,  for 
instance,  our  task  is  to  find  the  number  of  square  centi- 


6 


PHYSICAL  EXPERIMENTS. 


meters,  or  square  inches,  or  square  feet,  that  would  be  re- 
quired to  cover  it,  or  that  it  would  make  if  it  were  cut  up 
without  waste  into  squares.  In  this  case  the  square  centi- 
meter, or  square  inch,  or  whatever  square  we  choose  to 
take,  is  the  unit  of  surface.  We  might  set  about  to 
measure  surfaces  by  actually  placing  a  little  square,  a 
square  centimeter,  for  instance,  on  the  given  surface, 
marking  a  line  close  around  it,  then  moving  it  to  a  new 
place,  marking  around  it,  and  so  on  till  we  had  marked  off 
the  whole  surface  into  little  squares,  with  perhaps  some 
fractions  of  squares.  But  this  is  not  the  common  or  the 
best  way  of  measuring  surfaces.  The  common  way  is  to 
measure  the  length  of  certain  lines  on  the  surface  and 
from  the  lengths  of  these  lines  calculate  the  extent  of  the 
surface.  If  the  surface  is  in  the  form 
of  a  rectangle,  like  Fig.  2,  it  is  plain 
that  we  have  merely  to  multiply  the 
number  of  units,  centimeters  let  us  say, 
in  the  length  by  the  number  of  centi- 
meters in  the  width,  and  the  result, 
8  X  4  =  32  in  this  figure,  is  the  number  of  square  centi- 
meters into  which  the  surface  can  be  divided.  This  is 
called  the  extent  or  area  of  the  surface. 

In  the  next  two  Exercises  we  shall  undertake  to  find 
rules  for  the  measurement  of  surfaces  not  quite  so  simple 
in  shape  as  the  rectangle  shown  in  Fig.  2.  These  will  be 
parallelograms  and  triangks. 

A  parallelogram  is  a  flat  figure  bounded  by  four  straight 


Fig.  2. 


Fig.  3. 


lines,  each  line  being  parallel  to  the  line  opposite.     Thus 


MEASUREMENT  OF  DISTANCE,  ABE  A,  VOLUME.     7 

A  and  B  in  Fig.  3  are  parallelograms.  A  is  Avhat  we  have 
just  called  a  rectangle,  and  we  have  seen  how  to  find  the 
area  of  any  rectangle,  but  B  is  not  quite  so  simple  at  first 
sight.  A  parallelogram  like  B,  which  contains  no  right 
angle,  is  called  an  olliqtie  parallelogram. 

EXERCISE    3. 

AUEA  OF  AN   OBLIQUE  PARALLELOGRAM. 

Apparatus :  The  30-cm.  measuring-stick  (No.  3).  An  oblique 
parallelogram  of  paper  about  20  cm.  long  and  10  cm.  vride.  (One 
of  the  straight-edged  rulers  (No.  23)  may  prove  useful  in  this 
Exercise.) 

Draw  upon  the  paper  figure  a  line  like  c  in  Fig.  4,  taking 
care  to  make  a  right  angle  with  the 
top  line  and  the  bottom  line,  and  then 
cut  or  tear  the  paper  along  the  line  c. 
Take  the  small  piece  thus  removed 
and  join  it  to  the  larger  piece,  in  such 
a  way  as  to  make  a  figure  that  you 
knoTV  how  to  measure.     Measure  the  • 

length  and  width  of  the  figure  thus  formed  and  calculate  the 
extent  of  its  surface. 

Then  put  the  tw^o  pieces  together  as  they  were  at  first  and  ask 
yourself  whether  you  could  not,  if  another  parallelogram  were 
given  you,  find  the  extent  of  its  surface  without  cutting  it. 

Suggestions  for  the  Lecture-room. 

Have  the  pupils  estimate  without  measurement  the 
length  and  width  of  some  visible  and  convenient  rectangles, 
a  book-cover,  a  table-top,  a  window,  etc.,  and  calculate  the 
areas  from  these  estimated  dimensions.  Then  give  them 
the  true  dimensions  and  let  them  calculate  the  true  areas. 

EXERCISE    4. 

AREA    OF    PLANE   TRIANGLES. 

Apparatus :  Measuring-stick  (No.  3).  A  right  triangle  and  an 
oblique  triangle  of  thin  paper. 


8 


PHYSICAL  EXPERIMENTS. 


Take  the  right  triangle,  represented  "by  Fig.  5,  and  draw  upon 
it  a  line  d  parallel  to  the  base  line  ch,  beginning  at  a  point  mid- 

vray  between  d  and  b.  Fold 
the  paper  along  the  line  d  and 
then  tear  it  along  the  same 
line.  See  whether  you  can 
put  the  two  pieces  together  in 
the  form  of  a  rectangle.  If  so, 
meeisure  the  length  and  width 
of  this  rectangle,  then  put  the 
pieces  together  again  in  their 
original  position. 

We  shall  csJl  the  side  cb  the 

base  of  the  triangle,  and  the  side 

oft  the  height,  or  altitude.      Can  you  now  frame  a  rule  by  means 

of  which  you  can  find  the  area  of  a  right  triangle  wthout  cutting 

it? 

Now  take  the  other  triangle  abc,  Fig.  6,  and  draw  a  line  d 


Fio.  5. 


from  the  angle  a  in  such  a  direction  that  it  wrill  make  right  angles 
with  cb  at  e.  We  vnll  call  cb  the  base  of  the  -whole  triangle  and 
d  its  height.  This  line  d  has  now  divided  the  original  triangle 
into  two,  Jf  and  N,  each  of  which  is  a  right  triangle.  You  have 
already  learned  how  to  find  the  area  of  a  right  triangle.  You  can 
say  at  once  the 


area  of  M  ■ 

U  it     Jff, 


length  of 


X  .  .   .  length  of 
X  .  .  .      "  " 


area  of  -whole  triangle  =  .  .  .   X  .  .  .  length  of .  .  . 
You  can  now  frame  a  rule  for  finding  the  area  of  any  triangle. 


MEASUREMENT  OF  DISTANCE.  AREA,   VOLUME.      9 


Suggestions  for  the  Lecture 

Any  (jlane  figure  bounded  by 
straight  lines.  Fig.  ?,  for  in- 
stance, can  evidently  be  divided 
into  triangles  and  each  of  these 
triangles  can  be  measured.  The 
sum  of  the  areas  of  the  triangles 
will  be  the  area  of  the  whole 
figure.  We  see,  then,  how  to 
measure  the  area  of  any  plane 
figure  bounded  by  any  number 
of  straight  lines. 

Volume. 


•room. 


Fig.  7. 


We  have  now  to  speak  of  the  measurement  of  volume. 
The  unit  of  volume  may  be  the  cubic  centimeter,  or  the 
cubic  inch,  or  the  cubic  foot,  etc.  We  shall  generally  use 
the  cubic  centimeter  as  our  unit.    . 

AYe  mean,  then,  by  the  volume  of  a  body  the  number  of 
cubic  centimeters  that  could  be  made  of  that  body  if  it 
were  cut  up  without  waste,  as  one  might  cut  np  a  large 
piece  of  clay  or  putty.  In  the  case  of  a  body  whose  surface 
is  made  up  of  rectangles,  a  brick,  for  instance,  it  is  easy  to 
see  how  the  volume  may  be  calculated,  if  we  know  the 
length  and  the  width  and  the  thickness.  We  have  volume 
=  length  x  width  X  thickness.  If  the  body  is  of  less  reg- 
ular shape,  like  an  ordinary  stone  or  a  lump  of  coal,  it  is 
not  so  easy  to  calculate  its  volume  from  measurements  of 
length,  width,  and  thickness.  There  is,  however,  a  very 
easy  way  of  finding  the  volume  of  such  a  body  by  the 
use  of  water,  as  will  presently  be  seen.  It  is  easy  to  find 
the  volume  of  a  quantity  of  water  in  several  ways.  One 
way  is  to  pour  the  water  into  a  rectangular  box.  Then  we 
can  measure  its  length  and  width  and  depth  and  calculate 
its  volume.     Another  way  is  to  pour  it  into  a  glass  meas- 


10  PHYSICAL  EXPERIMENTS. 

uring-dish  having  marks  upon  it  to  tell  the  number  of 
cubic  centimeters  required  to  fill  it  to  certain  depths. 
Another  method  is  to  weigh  the  water,  for  it  is  known  that 
one  cubic  centimeter  of  water  weighs  one  gram.  Indeed 
this  is  the  definition  of  one  gram,  the  weight  of  a  cubic 
centimeter  of  water.*  If  the  balance  which  we  use  for 
weighing  reads  in  ounces  instead  of  grams,  we  shall  have 
to  remember  that  1  oz.  =  about  28.3  gm.,  so  that  1  oz.  of 
water  will  be  28.3  cubic  centimeters.  We  shall  commonly 
find  the  volume  of  a  body  of  water  by  weighing. 

We  will  now  try  the  water  method  of  finding  the  vol- 
ume of  a  body,  a  rectangular  solid.  We  will  find  its 
volume  by  the  water  method  and  also  by  direct  meas- 
urement and  calculation,  and  then  see  how  well  the  two 
results  agree.  This  will  test  the  water  method,  and  if  we' 
find  it  to  work  well,  we  can  use  it  with  irregular  solids 
which  we  cannot  measure  directly. 

EXERCISE  5. 

VOLUME  OF  A  RECTANGULAR  BODY  BY  DISPLACEMENT 
OF  WATER. 

Apparatus:  A  brass  can  (No.  5)  called  0  in  Fig.  8.  A  small 
catch-bucket  (No.  6)  called  p  in  Fig.  8.  A  spring-balance  (No. 
7).  A  rectangular  block  of  vrood  (No.  8)  so  loaded  as  to  sink  in 
water. 

Closing  the  overflow  tube  t  of  the  can  C,  pour  water  into  C  until 
it  is  filled  nearly  to  the  brim.  Then  open  the  tube  and  let  all  the 
water  flow^  out  that  w^ill  do  so,  catching  it  in  the  small  can  p. 
The  large  can  should  rest  steadily  upon  the  table,  but  the  small 
one  is  better  held  in  the  hand  'when  the  flow^  begins,  otherwise 
some  water  may  be  spilled.  About  one  minute  should  be  allowed 
for  the  flow^  and  the  dripping  which  follows. 

Throw  away  all  the  ■water  thus  caught  in  p,  and  then  weigh  p 
on  the  spring-balance  to  the  nearest  gram  or  the  nearest  tw^en- 

*  To  be  exact  one  must  add  at  4°  of  tJie  centigrade  scale  of  tempera- 
ture.   For  the  purpose  of  this  book  such  exactuess  is  uuuecessary. 


MEASUREMENT  OF  DISTANCE,  AREA,  VOLUME.   11 

tieth  of  an  ounce,  according  to  the  graduation  of  the  balance.* 
Then,  closing  the  tube  t  as  before,  lower  into  the  can  C  the 
wooden  block  until  it  rests  upon  the  bottom.    Then,  or  sooner  if 


Fig.  8. 


the  can  C  seems  likely  to  be  overflowed,  open  the  tube  t,  and  as 
before  catch  the  w^ater  that  runs  out  in  the  small  can  p.  The 
water,  Fig  9,  now  stands  just  as  high  in  C  as  it  did  just  before  the 


Fig.  9. 

block  was  put  into  it.  The  block  has  crowded  out  into  the  can  p 
just  its  own  bulk  of  water.  If,  then,  we  can  find  the  volume  of 
the  water  that  the  block  drove  over  into  p,  we  have  the  volume 
of  the  block  itself. 


*  Ordinary  small  spring-balauces  now  in  the  market  are  marked 
off  in  i-ounce  divisions,  which  are  about  i  inch  long.  The  pupil 
will  learn  to  estimate  the  position  of  the  pointer  when  it  falls  between 
two  lines,  so  as  to  read  to  about  -^^  of  an  ounce. 


12  PHYSICAL  EXPERIMENTS. 

Weigh  p  and  the  vrater  it  contains. 

Weight  of  small  can  and  water  =  . . . 
«        "      <«        "    empty        = 


"        "  water  alone  = 

If  the  w^eight  as  thns  found  is  in  grams,  it  is  equal  to  the  number 
of  cubic  centimeters  in  the  block.  If  the  weight  as  thus  foiuid  is 
in  ounces,  'we  must  mtdtiply  the  number  of  ounces  by  28.3  in 
order  to  find  the  number  of  cubic  centimeters  in  the  block. 

Now  measure  carefully  the  length,  -width,  and  thickness  of  the 
block  and  calculate  the  number  of  cubic  centimeters  it  contains 
from  these  measurements. 

(Experiments  for  finding  the  volumes  of  irregular  bodies  by 
the  water  method  may  w^ell  be  postponed  till  the  next  Exercise, 
-which  would  otherwise  be  a  very  brief  one.  Potatoes,  stones, 
lumps  of  coal,  etc.,  of  suitable  size  may  be  used  for  these  further 
experiments.) 

Suggestions  for  the  Lecture-room. 

Give  simple  questions  and  problems,  to  be  answered  at 
once,  upon  the  preceding  Exercises. 

Draw  a  line  10  inches  long  on  the  blackboard,  divide  it 
by  a  cross-line  at  any  point,  and  ask  the  class  to  estimate 
the  distance  from  either  end  to  this  cross-line. 

Show  how  to  test  the  correctness  of  the  spring-balances 
by  hanging  known  weights  upon  them,  2  ounces,  4  ounces, 
8  ounces,  for  instance. 


DENSITY  AND  SPECIFIC  GRAVITY.  13 


CHAPTER  11. 
DENSITY  AND  SPECIFIC  GRAVITY:    FLUID  PRESSURE. 

EXERCISE  6. 

WEIGHT  OF  UNIT  VOLUME  OF  A  SUBSTANCS. 

Apparatus :  A  block  of  wood  (No.  9).  A  spring-balance  (No. 
7).     A  measuring-stick  (No.  3).    Thread  for  suspending  the  block. 

Find  the  'weight  of  the  block  in  grams  and  also  in  ounces. 

Measure  the  length  of  each  of  the  four  edges  which  are  parallel 
to  the  grain  of  the  wood,  take  the  average  of  these  measurements 
and  call  it  the  length  of  the  block. 

Measure  the  length  of  each  of  the  four  long  edges  which  are 
crosswise  to  the  grain  of  the  wood,  and  call  the  average  of  these 
four  measurements  the  tcidth  of  the  block. 

Measure  the  length  of  each  of  the  four  short  edges  and  call  the 
average  of  these  four  measurements  the  thickness  of  the  block. 

The  weight  in  ounces  is  to  be  turned  into  pounds. 

From  the  length,  width,  and  thickness  in  centimeters  the  length, 
width,  and  thickness  in  feet  may  be  found  by  the  rule  that  1  ft.  = 
30.5  cm.,  but  it  is  shorter  to  find  the  volume  in  feet  from  the  vol- 
ume in  cubic  centimeters  by  the  rule  that  1  cu.  ft.  =  28300  cu.  cm. 

Calculate,  1st,  how  many  grams,  or  what  part  of  a  gram,  1  cu. 
cm.  of  the  block  weighs ;  2d,  how  many  pounds,  or  what  part  of 
a  pound,  1  cii.  ft,  of  such  wood  weighs. 

Suggestions  for  the  Lecture-room. 

The  weight  of  uuit  volume  of  a  substance  is  called  the 
Density  of  the  substance. 

We  have  found  that  the  density  of  a  body  in  gram  and 
centimeter  units  is  not  the  same  as  the  density  of  the  same 
body  in  pound  and  foot  units. 

The  weight  of  1  cu.  cm.  of  water  is  1  gram;   but  the 


14  PHYSICAL  EXPERIMENTS. 

weight  of  1  cu.  ft.  of  water  is  about  62.4  pounds.  This  is 
a  useful  fact  to  remember. 

What  ratio  has  the  class  found  between  the  density  of 
wood  in  pounds  and  feet  and  its  density  in  grams  and 
centimeters  ? 

If  we  know  the  density  of  a  substance  we  can  calculate 
the  weight  of  any  Tolume  of  that  substance.  Engineers 
and  other  scientific  men  often  have  to  find  by  this  method 
the  weight  of  objects  which  it  would  be  inconvenient  to 
weigh.  The  weights  of  buildings  and  bridges,  for  instance, 
are  found  in  this  way.  Books  used  by  scientific  men  con- 
tain tables  giving  the  densities  of  many  different  sub- 
stances. 

Often  we  find  it  useful  to  know  the  ratio  between  the 
tveigJit  of  a  body  and  the  zoeight  of  an  equal  hulk  of  boater, 
and  we  shall  have  soon  a  number  of  Exercises  showing  how 
this  ratio  may  be  found.  Before  we  come  to  these  we  shall 
need  to  go  through  one  or  two  preliminary  Exercises  to 
make  us  better  acquainted  with  the  force  exerted  by  water 
upon  bodies  floating  or  immersed  in  it. 

Before  going  farther  we  need  to  think  carefully  about 
the  meaning  of  the  word  lueight,  which  we  have  already 
used  a  number  of  times  and  shall  have  to  use  very  often. 
The  word  has  two  meanings. 

Sometimes  when  we  speak  of  the  weight  of  a  body  we 
mean  the  amount  of  the  body,  as  when  we  speak  of  10  lbs. 
of  butter  or  100  lbs.  of  iron. 

At  other  times  we  mean  by  the  weight  of  a  body  the 
amount  of  the  earth's  downward  pull  upon  that  body,  as 
shown  by  the  spring-balance,  for  instance. 

It  is  somewhat  hard  to  remember  this  distinction,  be- 
cause the  units  in  which  we  tell  the  amount  of  a  body 
have  the  same  name  as  the  units  in  which  we  tell  the  pull 
which  the  earth  exerts  upon  the  body.  For  instance,  we 
say  that  the  earth  exerts  a  pull,  or  force,  of  5  lbs.  upon 


DENSITY  AND  SPECIFIC  GRA  VlTY.  15 

5  lbs.  of  wood,  or  5  lbs.  of  coal,  or  anything  which  consists 
of,  or  is,  5  lbs.  of  substance. 

Often  when  we  use  the  word  weiglit  it  makes  no  differ- 
ence which  of  its  two  meanings  we  have  in  mind,  but 
sometimes  it  does  make  a  difference.  Thus,  when  we  put 
a  body  under  water,  as  we  shall  do  in  the  next  Exercise, 
and  say  that  it  loses  in  apparent  weight  in  going  from  air 
to  water,  we  do  not  mean  that  there  appears  to  be  any  less 
of  the  body  in  water  than  there  was  in  air.  We  mean  that 
it  requires  a  smaller  pull  of  the  spring-balance  to  keep  the 
body  from  sinking  in  water  than  it  does  to  keep  it  from 
sinking  in  air. 


EXERCISE  7. 

LIFTING  EFFECT  OF  WATER  UPON  A  BODY  ENTIRELY  IMMERSED 

IN  IT. 

Apparatus:  Overflow-can  (No.  5).  Oatch-bucket  (No.  6).  Spring- 
balance  (No.  7).     Loaded  block  (No.  8).     Thread. 

Fill  the  can  and  let  it  overflow  and  drip  for  one  minute  as  in 
Exercise  5.  Catch  this  overflow  in  the  small  bucket  and  throve  it 
aw^ay.     Then  weigh  the  empty  bucket  in  grams. 

Weigh  the  block  in  grams  before  immersing  it  in  the  water. 

Lower  the  block,  still  suspended  from  the  balance,  into  the 
overflow-can  till  it  is  entirely  covered,  catching  the  overflow 
and  saving  it. 

Weigh  the  block  in  the  water,  the  balance  being  entirely  above 
the  water. 

Weigh  the  bucket  ivith  the  overflowed  w^ater. 

Subtract  the  (apparent)  w^eight  of  the  block  in  water  from  its 
weight  in  air,  and  call  the  difference  the  loss  of  weigld  of  the  block 
in  water,  or  the  buoyant  force  exerted  upon  the  block  by  the  water. 

Find  weight  of  the  w^ater  in  the  small  bucket,  and  compare  this 
with  the  loss  of  weight  of  the  block  in  water. 

If  there  is  time,  make  a  similar  experiment  with  other  bodies. 

The  law  illustrated  in  this  Exercise  is  called  from  its  discoverer 
the  law,  or  principle,  of  Archimedes.  (See  any  encyclopedia  for  an 
account  of  Archimedes.) 


16  PHYSICAL  EXPERIMENTS. 


Suggestions  for  the  Lecture-room. 

Fill  the  gallon  glass  jar  (No.  10)  with  water  to  a  level 
ahout  one  inch  from  the  top.  Close  the  smaller  end  of  a 
student  lamp-chimney  tight  with  a  good  cork  stopper. 
Make  the  pressure-gauge  (No.  I.)  ready  for  use  by  the 
following  operation,  having  first  put  on  a  fresh  rubber 
diaphragm  if  necessary:  Release  the  glass  tube  from  the 
rubber  tube  and  wet  the  whole  length  of  the  glass  tube 
inside  with  water,  leaving  within  it,  about  one  inch  from 
one  end,  a  column  of  water  about  one-half  inch  long  to 
serve  as  an  index.*  Hold  the  gauge  itself  under  water  for 
a  little  time  before  reconnecting  the  glass  tube  with  the 
rubber  tube,  in  order  to  allow  the  air  within  the  gauge  to 
come  to  the  temperature  of  the  water.  Now  push  the 
gauge  down  into  the  jar  and  raise  and  lower  it  repeatedly 
in  the  water,  keeping  the  glass  tube  with  the  water-index 
horizontal,  and  let  the  class  determine  from  the  move- 
ments of  this  index  whether  the  pressure  of  the  water 
against  the  rubber  diaphragm  increases  or  decreases  when 
the  gauge  is  pushed  deeper  in  the  water. 

Rest  the  bottom  of  the  wooden  pillar  of  the  gauge  upon 
the  bottom  of  the  jar,  and,  still  keeping  the  glass  tube 
horizontal,  turn  the  upper  pulley  so  that  by  means  of  the 
rubber  band  the  lower  pulley  will  be  turned  and  the 
rubber  diaphragm  will  face  downward  sidewise  and  upward 
in  succession,  its  centre  remaining  practically  unchanged 
in  position.  Let  the  class  determine  by  watching  the 
water-index  whether  the  pressure  upon  the  rubber  dia- 
phragm is  any  greater  when  it  faces  upward  than  when 
it  faces  downward  or  sidewise. 

Push  the  closed  end  of  the  lamp-chimney  down  into  the 

*  It  may  be  necessary  to  use  water  colored  by  some  aniline  dye 
before  a  large  class. 


BEmiTT  AND  SPECIFIC  QRAVlTT.  17 

water  till  it  is  near  the  bottom  of  the  jar.  Move  the 
gauge-face  about,  without  changing  its  level,  so  as  to  bring 
it  under  this  closed  end.  Move  it  now  out  of  and  now 
into  this  position,  thus  changing  the  depth  of  water  im- 
mediately above  it  from  one-half  inch  or  less  to  several 
inches.  Let  the  class  determine  by  watching  the  index 
whether  such  changes  of  position,  without  change  of  lei^el, 
make  any  difference  in  the  pressure  against  the  gauge-face. 

We  shall  make  considerable  use  farther  on  of  the  facts 
brought  out  by  these  experiments.  Just  here  we  can  see 
that  they  explain,  at  least  in  a  general  way,  why  a  body 
immersed  in  water  weighs,  or  appears  to  weigh,  less  than 
when  in  the  air.  For  we  see  that  there  is  an  upward  press- 
ure of  the  water  against  the  under  side  of  the  body,  and 
that  this  upward  pressure  is  greater  than  the  downward 
pressure  against  the  upper  side  of  the  body. 

Having  seen  that  there  is  greater  pressure  on  low  levels 
than  on  high  levels  in  water,  we  may  well  ask  whether  this 
greater  pressure  crowds  the  particles  of  water  closer  together 
on  the  low  levels,  thus  making  the  water  denser  than  on 
high  levels.  In  fact  there  is  an  effect  of  this  kind,  but  it  is 
so  slight  that  we  need  take  no  account  of  it  in  any  ordinary 
case.     It  is  very  difficult  to  compress  water  much. 

EXPERIMENT. 

Fill  a  bottle  with  water  and  close  it  with  a  rubber  stop- 
per, leaving  one  hole  through  it.  Then,  holding  the  stop- 
per firmly  in  place,  try  to  push  into  the  hole  a  solid  brass 
rod  of  a  size  to  fit  rather  closely.     (App.  No.  II.) 

We  have  not  made,  and  cannot  well  make  with  the  gauge 
just  used,  any  accurate  measurement  of  the  rate  at  which 
pressure  changes  with  change  of  level  in  water.  The  fact 
is,  however,  that  if  we  place  a  surface  of  1  sq.  cm.  hori- 


18  •      PHYSICAL  EXPERIMENTS. 

zontal  at  any  depth  in  water  the  column  of  water  just 
above  it  is  resting  upon  the  given  surface.*  If  we  carry 
the  given  surface  down  1  cm.  farther,  we  now  have  resting 
upon  it  a  load  somewhat  greater  than  before,  greater  by  the 
weight  of  the  additional  1  cu.  cm.  of  water  which  is  now 
above  it.  As  1  cu.  cm.  of  water  weighs  1  gm.,  the  press- 
ure upon  a  surface  of  1  sq.  cm.  changes  by  1  gm.  for  each 
1  cm.  change  of  level  in  the  water. 

EXERCISE    8. 
WEIGHT  OF  WATER  DISPLACED  BY  A  FLOATING  BODY. 

Apparatus :  The  same  as  in  the  preceding  Exercise,  with  the 
exception  of  the  sinking  body,  which  is  here  replaced  by  one  that 
floats  (No.  4). 

Weigh  the  cylinder,  in  grams,  in  air.  Find,  in  grams,  the 
weight  of  water  which  it  displaces  from  the  overflow-can.  .  Com- 
pare these  two  weights. 

Suggestions  for  the  Lecture-room. 

We  have  made  some  experiments  with  liquid-pressure. 
We  must  now  begin  to  learn  something  about  air-pressure, 
which  in  many  practical  matters  of  every-day  life  has  a  very 
important  connection  with  water-pressure.  We  will  at  the 
start  repeat  in  a  slightly  varied  form  a  famous  experiment 
first  made  by  Torricelli,  an  Italian,  about  250  years  ago. 

EXPERIMENTS. 

Take  two  pieces  of  strong  glass  tubing  about  0.7  cm.  in 
inside  diameter,  one  of  them,  about  1  m.  long,  closed  at  one 
end,  the  other,  about  20  cm.  long,  open  at  both  ends,  and 
connect  them  by  means  of  a  thick-walled  piece  of  rubber 

*  The  pressure  upon  the  given  surface  may  be  greater  than  the 
weight  of  the  column  of  water  resting  upon  it,  for  there  ma\'  be,  and 
usually  is,  a  downward  pressure  of  air  or  something  else  upon  the 
top  of  the  water-column. 


DENSITY  AND  SPECIFIC  GRAVITY.  19 

tubing  about  25  cm.  loug.  The  rubber  tube  should  fit 
tight  upou  the  glass  tubes,  and  for  gi-eater  security  sliould 
be  fastened  on  by  means  of  wire  or  string. 

Holding  the  tubes  thus  connected  (App.  No.  III.)  by  the 
free  end  of  the  short  glass  tube,  the  closed  end  of  the  long 
glass  tube  hanging  down,  pour  mercury  by  means  of 
a  small  funnel  of  glass  or  paper  into  the  tubes,  tap- 
ping or  shaking  them  occasionally  to  dislodge  air- 
bubbles,  until  the  top  of  the  mercury-column  reaches 
the  rubber  tube.  Then  gently  raise  the  closed  end 
of  the  long  glass  tube  until  this  tube  points  straight 
upward  (Fig.  10),  meanwhile  holding  the  other 
glass  tube  upright  and  taking  care  that  no  mer- 
cury is  spilled. 

During  the  latter  part  of  this  operation  it  will 
be  noticed  that  the  mercury  begins  to  fall  away 
from  the  closed  end  of  the  long  glass  tube,  and 
finally  several  inches  of  this  tube  will  be  appar- 
ently empty.  (Really  this  space  contains  a  very 
little  air,  from  the  bubbles  that  were  in  the  mer- 
cury-column before  it  was  inverted,  but  so  little  ^°'  ^^' 
that  we  may  at  present  disregard  it  and  consider  the  space 
above  the  mercury  as  empty.  Such  a  space  is  called  a  vac- 
uum, from  a  Latin  word  meaning  emjjty.)  But  the  mer- 
cury continues  to  stand  very  much  higher  in  the  long  glass 
tube  than  in  the  short  one.  It  was  known  before  the 
time  of  Torricelli  that  if  air  was  drawn  out  from  a  tube  the 
lower  end  of  which  rested  in  water,  the  water  would  rise  in 
the  tube,  but  the  true  reason  for  this  was  not  known.  Tor- 
ricelli maintained,  and  Pascal,  a  Frenchman,  showed  by 
experimenting  at  different  heights  in  the  air,  that  the 
pressure  of  the  atmosphere,  due  to  its  weight,  accounted 
for  the  rise  of  liquids  in  a  vacuum.  We  have  only  to 
think  of  the  fact  that  the  air,  although  its  density  is  very 
small  compared  with  that  of  water^  has,  because  of  its  great 


^ 


20 


PHYSICAL  EXPERIMENTS. 


quantity,  a  great  weight,  and  we  see  that  the  air,  pressing 
upon  the  mercury  surface  in  the  shorter  tube,  balances 
the  column  of  mercury  in  the  long  tube. 

By  measuring  the  difference  in  height  of  the  two  mer- 
cury surfaces  we  can  get  a  measure  of  the  atmospheric 
pressure.  "We  find  that  the  atmospheric  pressure  is  about 
as  great  upon  the  surface  of  the  earth  as  would  be  the 
pressure  of  a  layer  of  mercury  7G  cm.  deep,  or  a  layer  of 
water  about  10.3  m.  deep,  over  the  whole  earth.  The 
pressure  per  square  centimeter  at  any  given  part  of  the 
earth's  surface  varies  somewhat  from  day  to  day  and  even 
from  hour  to  hour. 

If  we  fasten  the  apparatus  that  has  just  been  used  to 
a  suitable  support  it  will  serve  as  a  fairly  good  barom- 
eter. 

Air-pressure,  like  liquid-pressure,  is  at  any  given  point 
equal  in  all  directions,  if  the  air  is  at  rest. 


Take  a  strong  thistle-tube  (No. 
j^'^\  \^j   IV.)  of  the  shape  shown  in  Fig.  11 

and  tie  a  piece  of  thick  sheet  rubber 
across  the  mouth,  which  may  be  about 
1  inch  in  diameter.  Make  the  cover- 
ing air-tight  by  means  of  some  cem- 
ent, melted  beeswax  and  rosin,  for 
instance,  poured  in  at  the  joint  /. 
Connect  this  thistle-tube  by  means  of 
a  thick-walled  rubber  tube  to  an  air- 
pump  (No.  v.),  and  exhaust  the  air. 
The  rubber  cap,  not  being  supported 
by  air-pressure  beneath,  will  now  be 
pushed  down  by  the  atmospheric 
pressure  into  a  deep  cup-shape.  Pinch 
the  rubber  tube  so  that  no  air  shall 
leak  back  into  the  thistle-tube,  and  then  turn  the  mouth 


Fia.  11. 


DENSITY  AND  SPECIFIC  GRAVITY.  21 

of  the  latter  in  all  directions,  sidewise,  downward,  and 
oblique.  Observe  whether  the  form  of  the  rubber  cup 
changes  during  this  operation,  as  it  would  do  if  the  press- 
ure upon  it  changed. 

We  should  find  by  proper  experiments  that  in  air  at 
rest,  as  in  water  at  rest,  pressure  is  equally  great  at  all 
points  on  the  same  level.  We  should  find,  also,  that  the 
air-pressure  diminishes  with  increase  of  height  from  the 
earth's  surface,  but,  as  the  density  of  air  is  very  little 
compared  with  that  of  water,  it  requires  a  consider- 
able change  of  level  to  make  much  difference  in  the  air- 
pressure. 

Substances  which,  like  water  and  air,  press  equally  in  all 
directions  at  a  given  point  and  are  easily  changed  in  shape 
are  cd\\e(\.  fluids,  that  is,  substances  that  can  flow.  Other 
substances,  like  wood,  iron,  stone,  etc.,  which  do  not  flow 
from  one  shape  to  another  are  called  solids. 

Fluids  are  divided  into  two  classes :  liquids  and  gases. 
Water,  oil,  milk,  kerosene,  etc.,  are  liquids.  Air  is  a  mix- 
ture of  several  gases.  Liquids  are  much  heavier  than 
gases,  in  most  cases.  Most  liquids  are  easily  seen.  Most 
gases  are  practically  invisible.  But  perhaps  the  most 
striking  difference  between  liquids  and  gases  is  a  difference 
in  compressibility.  We  have  seen  that  it  is  difficult  to 
compress  water  much,  but  it  is  very  easy  to  compress 
air. 

Take  the  bent  glass  tube  (No.  VI.),  closed  at  one  end, 
and  pour  into  it  a  little  mercury,  enough  to  fill  the 
bend.  At  first  the  mercury  will  stand  a  little  higher 
in  the  long  arm,  but  by  tipping  the  tube  and  letting 
out  a  little  of  the  air  imprisoned  in  the  short  arm  the 
level  can  be  made  nearly  the  same  in  both  arms,  as  in 
Fig.  13.    Now  measure  the  length  of  the  imprisoned  air- 


22  PHYSICAL  EXPERIMENTS. 

column,  and  write  it  under  the  letter  F*  on  the  black- 
board. 

V.  P.  F  X  P. 


The  pressure  upon  this  air  is  now,  if  the  mer- 
cury level  is  the  same  in  both  arms,  equal  to 
that  upon  the  unimprisoued  air.  It  is  as  great 
a  pressure  as  would  be  exerted  by  the  weight  of 
a  column  of  mercury  as  tall  as  that  in  the  barom- 
eter (Fig.  10).  Take,  then,  a  reading  of  this 
barometer  and  record  this  reading  under  the 
ty)  letter  P. 
Fio.  12.  Pour  in  more  mercury  till  the  difference  of 
level  in  the  two  arms  is  about  20  cm.,  then  measure  again 
the  length  of  the  inclosed  air-column.  Record  this  length 
under  V,  and  record  under  P  the  present  difference  of  mer- 
cury level  2)lus  the  height  of  the  barometer  column. 

Proceed  by  stages  in  this  way  till  the  volume  of  the  in- 
closed air-column  is  about  one  half  what  it  was  at  first. 
Multiply  each  number  under  V  by  the  correspondiug 
number  under  P,  and  write  the  products  in  the  column 
headed  V  X  P.  An  examination  of  this  last  column  will 
probably  indicate  a  very  simple  law  connecting  pressure  and 
volume  in  the  case  of  any  given  body  of  air.  This  law  is 
important,  and  should  be  remembered  by  the  pupil.  It  is 
sometimes  called  Boyle's  law  and  sometimes  Mariotte's 
law.     We  shall  call  it  by  the  shorter  name,  Boyle's  laio. 

*  The  length  of  the  air-column  is  the  same  as  its  volume,  if  we  lake 
for  our  uuit  of  volume  the  space  coutaiued  in  unit  length  of  the  tube. 


DENSITY  AND  SPECIFIC  GRAVITY. 


23 


EXERCISE   9. 

RATIO  BETWEEN  THE  WEIGHT  OF  A  SOLID  BODY  AND  THE 
WEIGHT  OF  AN  EQUAL  BULK  OF  WATER. 

Apparatus :  The  spring-balance  (No.  7).  The  gallon  jar  (No.  10) 
nearly  filled  with  water.     A  lump  of  sulphur  (No.  11).    Thread. 

Weigh  the  sulphur  in  air ;  then  in  water. 

We  know  from  Exercise  7  that  a  body  immersed  in  water  loses 
in  apparent  weight  an  amount  equal  to  the  weight  of  the  water 
whose  place  it  has  taken.  It  is  easy,  therefore,  to  get  from  the 
two  weighings  just  made  the  ratio  which  we  have  undertaken  to 
find  in  this  exercise. 

This  ratio  is  called  the  specific  gravity  of  sulphur  as  compared 
with  w^ater.  We  shall  have  a  number  of  exercises  for  finding 
specific  gravities  by  other  methods.  {Gravity  comes  from  a  Latin 
word  gravis,  meaning  heavy.  Specific  means  distinct,  or  particuldr. 
The  specific  gravity  of  a  body  is  its  particular  fieaviness — the  heavi- 
ness which  distinguishes  this  body  from 
other  bodies  of  equal  size.) 

If  time  permits,  find  in  this  Exercise,  by 
the  same  method  that  was  used  for  the 
sulphur,  the  specific  gravity  of  other  solids 
that  will  sink  in  water — glass,  coal,  etc. 

Suggestioiis  for  the  Lecture-room. 


QUESTIONS. 

A  cubical  box,  10  cm.  along  each 
edge,  has  extending  from  its  top,  as 
in  Fig.  13,  a  tube  15  cm.  tall  and  1 
sq.  cm.  in  cross-section  (inside).  If 
the  box,  but  not  the  tube,  is  full  of 
water,  how  great  is  the  water-pressure 
on  the  whole  of  the  bottom  ? 

If  the  tube  as  well  as  the  box  is  full 
of  water,  how  great  is  the  pressure 
upon  that  one  sq.  cm.  of  the  bottom  which  lies  just  be 
jieath  the  tube  ? 


Fig.  13. 


24  PHYSICAL  EXPERIMENTS. 

Is  the  pressure  equally  great,  per  sq.  cm.,  at  other  parts 
of  the  bottom  ? 

How  much  is  the  total  pressure  now  on  the  bottom 
of  the  box  ? 

How  great  is  the  pressure  per  sq.  cm.  at  the  top  of  the 
box  just  at  the  bottom  of  the  tube  ? 

How  great  is  the  total  nptcard  pressure  of  the  water 
against  the  top  of  the  box  ? 

(Disregard  the  atmospheric  pressure  upon  the  top  of  the 
water-column  in  all  these  questions  at  first.  Afterward 
call  this  atmospheric  pressure  1000  gm.  per  sq.  cm.,  and 
ask  the  same  questions  as  before.) 

EXPERIMENTS. 

The  preceding  questions  bring  out  the  fact  that  by 
exerting  pressure  in  a  small  tube  connected  with  a  large 
vessel,  both  being  filled  with  water,  one  can  increase  corre- 
spondingly the  pressure  throughout  the  vessel.  The  fol- 
lowing experiment  will  show  that  similar  effects  can  be 
produced  with  air-pressure  :  Take  a  common  rubber  foot- 
ball and  blow  air  into  it  till  it  is  about  half  filled,  con- 
necting a  rubber  tube  with  the  key  for  greater  convenience 
in  blowing  (App.  No.  VII.).     Then  rest  one  end  of  a  board. 


Fio.   14. 

as  in  Fig.  14,  on  the  football  and  the  other  end  upon  a  box 
or  block  of  about  the  same  height.  Then  place  a  weight  of 
25  lbs.  or  more  on  the  board  nearly  over  the  ball,  holding 
the  rubber  tube  attached  to  the  key  in  such  a  way  that  the 
air  cannot  escape  from  the  ball.  Then  blow  through  the 
tube  into  the  ball  and  observe  that  you  can  in  this  way  lift 
the  weight. 


DENSITY  AND  SPECIFIC  GRAVITY.  25 

The  experiment  illustrates  the  operation  of  the  hydro- 
static press,  a  machine  in  which  a  very  great  force  is  ob- 
tained, for  lifting  or  compressing  bodies,  by  pumping  water 
through  a  small  tube  into  a  large  cylinder,  one  end  of  which 
is  closed  by  a  movable  stopper  called  a  piston. 

Take  again  the  pressure-gauge  and  the  accompanying  ap- 
paratus used  in  the  experiments  following  Exercise  7.  Fill 
the  lamp-chimney  with  water,  and  then,  holding  a  card 
across  the  open  end,  invert  the  chimney,  lower  the  end  cov- 
ered by  the  card  into  the  water,  and  then  remove  the  card. 
Most  of  the  water  will  now  remain  in  the  chimney,  although 
its  upper  end  is  nine  or  ten  inches  above  the  surface  of  the 
water  in  the  jar. 

How  does  the  pressure  per  sq.  cm.  inside  the  chimney 
on  a  level  with  the  outside  water-surface  compare  with  the 
pressure  per  sq.  cm.  at  this  outer  surface,  that  is,  the 
atmospheric  pressure?  How,  then,  will  the  pressure  per 
sq.  cm.  at  points  higher  in  the  chimney  compare  with  the 
atmospheric  pressure  ?  After  answering  these  questions  by 
the  aid  of  what  the  class  already  knows  about  liquid  press- 
ure, test  the  correctness  of  the  answer  by  means  of  the 
gauge.  (The  gauge  as  mounted  for  previous  experiment 
is  rather  inconvenient  for  this  experiment  with  the  lamp- 
chimne}',  and  it  would  be  well  to  detach  it  from  the  wooden 
support  if  this  can  be  done  readily.) 

Take  a  long  narrow  glass  tube  open  at  both  ends,  and 
dip  one  end  into  a  vessel  of  water.  Apply  the  lips  to  the 
other  end  and  draw  the  water  up  till  the  tube  is  filled.  Ask 
the  class  to  explain  the  operation.  In  what  sense  is  the 
water  drawn  up  ?  (The  operation  begins  with  an  ex- 
pansion of  the  lungs  which  lessens  the  air-pressure  within 
them.  Then  air  runs  from  the  place  of  high  pressure,  the 
tube,  to  the  place  of  low  pressure,  the  lungs.  So  the  air- 
pressure  within  the  tube  is  lessened.) 


26  PHYSICAL  EXPERIMENTS. 

After  filling  the  tube  in  tliis  way  quickly  close  the  top 
with  a  finger  and  then  lift  the  lower  end  from  the  water. 
Take  off  the  finger  for  an  instant,  then  replace  it. 

Fill  or  nearly  fill  a  tumbler  or  broad-mouthed  bottle 
with  water  and  then  cover  it  with  a  sheet  of  thick  paper. 
Hold  the  paper  firmly  in  place  with  the  hand  and  invert 
the  tumbler;  then  take  away  the  hand  that  holds  the  paper. 
As  accidents  may  happen,  the  tumbler  should  be  held  over 
some  large  dish. 

EXERCISE   lO. 

SPECIFIC  GRAVITY  OF  A  BLOCK  OF  IVOOD  BY  USE  OF  A  SINKER. 

Apparatus :  A  rectsmgular  block  of  wood  (No.  9).     The  spring- 
balance  (No.  7).   The  gallon  jar  (No.  10)  nearly  filled  with  water. 
A  lead  sinker  (No.  12).     Thread. 
By  definition  (Exercise  9)  we  have 

_  Wt.  of  the  body 

P'  °       '  ^  ~  Wt.  of  an  equal  volume  of  water' 

Exercises  5  and  7  show  us  that  the  quantity  written  below  the 
line  in  this  definition  may  be  expressed  in  other  ways.     We  may 
write 
Sp.  grav.  of  a  body 

Wt.  of  the  body 

~  Wt.  of  water  displaced  by  the  body  when  immersed 
or 

Wt.  of  the  body 


Sp.  grav.  = 
or 
Sp.  grav.  = 


IjOss  of  weight  of  the  body  when  immersed 
Wt.  of  the  body 


liifting  effect  of  water  upon  the  body  when  immersed 

These  expressions  all  mean  the  same  thing,  but  sometimes  one 
of  them  is  more  convenient  than  the  others.  In  the  exercise  now^ 
before  us  we  shall  use  the  last  form. 

We  have  to  find  two  quantities,  by  experiment:  1st,  the  weight 
of  the  body  ;  2d,  the  lifting  effect  of  water  ^ipon  it  when  immersed. 

Weigh  the  wood  in  air  and  record  its  w^eight. 

Now  put  the  block  into  water.    You  see  that  it  floats.    To  make  it 


DENSITY  AND  SPECIFIC  GRAVITY. 


"21 


stay  under  water  you  must  liold 
it  d(no)i.  Try  this,  putting  your 
fingers  on  the  block.  In  this 
case,  you  see,  the  lifting  effect 
of  the  water,  when  the  block  is 
wholly  beneath  its  surface,  is 
greater  than  the  weight  of  the 
block.  We  will  try  to  find  out 
how  much  it  is. 

We  shall  use  the  lead  sinker 
to  hold  the  block  under  water, 
and  we  need  to  know  the  weight 
of  the  sinker  alone  under  water. 
Weigh  it  in  this  position  and 
record  the  w^eight. 

Now  suspend  the  block  from 
the  balance  *  and  the  lead  sinker 
from  the  thread  under  the  block, 
and  consider  how  much  the  two, 
block  and  sinker,  would  weigh 
in  the  position  shown  by  Fig. 
15,  the  block  out  of  w^ater  and 
the  sinker  in  water.  You  can 
tell  this  from  the  w^eighings  al- 
ready made.     Write  it   down : 

Wt.  of  block  in  air  -\-  Wt.  of 
sinker  in  water  =  ....  -j- ...  . 

Now  low^er  the  block  and 
sinker    till    both    are    covered 


Fig.  15. 


*The  success  of  a  difficult  experiment  like  this 
depends  greatly  upon  the  care  with  which  the  details 
of  the  work  are  thought  out  by  the  teacher.  The  fol- 
lowing method  of  attaching  the  block  to  the  balance  is 
recommended:  Take  a  thread  two  feet  long  and  tie 
the  ends  together.  Then  make  of  it  a  slip-noose  by 
passing  one  end,  I  (Fig.  16),  through  the  other  end, 
k.  The  block  may  then  be  placed  in  the  noose  and 
the  loop  I  slipped  upon  the  hook  of  the  balance, 
but  to  prevent  slipping  when  the  lead  weight  is  to 
be  suspended  from  the  loop  below  the  block  it  is 
well  to  pass  the  loop  I  twice  through  at  k. 


Fig.  16. 


28  PffYSTOAL  tlXPKRIMBNTS, 

by  the  water,  and  weigh  the  two  together  in  this  position  and 
record  : 

Wt.  of  block  and  sinker  together  in  water  =    .  .  .  . 

Just  before  the  block  entered  the  water,  the  sinker  being  already 
in,  the  'weight  was  ....  Just  as  soon  as  the  block  also  'was 
covered  the  w^eight  was  only  ....  The  difference  is  the  lifting 
effect  of  the  water  upon  the  block.  We  have  now  all  that  we  need  for 
calciilating  the  specific  gra'vity  of  the  block  by  means  of  the 
formula  already  given, 

fl«  «^»^  Wt.  of  block 

Sp.  grav.  = 


Lifting  effect  of  water  upon  block  immersed 

Suggestions  for  the  Lecture-room. 
Review  questions  on  liquid  pressure  and  specific  gravity. 

PROBLEMS. 

(1)  A  brick-shaped  body  20  cm.  long,  10  cm.  wide, 
and  5  cm.  thick  weighs  1500  grams.  What  is  its  density 
in  gram  and  centimeter  units  ? 

What  would  be  the  weight  of  an  equal  bulk  of  water  ? 
What,  then,  is  the  specific  gravity  of  this  body  ? 

(2)  A  body  whose  volume  is  700  cu.  cm.  has  the  density  8 
in  gram  and  centimeter  units.  How  much  does  it  weigh  ? 
What  is  its  specific  gravity  ? 

(3)  A  body  20  ft.  long,  10  ft.  wide,  and  5  ft.  thick 
weighs  93,600  lbs. 

What  is  its  density  in  pound  and  foot  units  ? 

What  would  be  weight  of  an  equal  bulk  of  water,  one 
cu.  ft.  of  water  weighing  62.4  lbs.  ?  What,  then,  is  the 
specific  gravity  of  the  body  ? 

(4)  A  body  whose  volume  is  700  cu.  ft.  has  the  density 
499.2  in  pound  and  foot  units.  How  much  does  it  weigh  ? 
What  is  its  specific  gravity  ? 

What  numerical  relation  do  we  find  in  the  preceding 


DENSITY  AND  SPEGIFIG  GRAVITY. 


29 


l)roblems  between  density  in  gram  and  centimeter  units 
and  specific  gravity  ? 

What  relation  between  density  in  pound  and  foot  units 
and  specific  gravity  ? 


EXPERIMENT. 

Fig.  17  (App.  No.  VIII.)  shows  a  bottle 
closed  with  a  rubber  stopper  through  which 
two  glass  tubes,  a  and  b,  open  at  both  ends, 
extend.  To  one  of  the  tubes,  a,  is  attached 
a  rubber  tube,  r.  The  bottle  and  the  two 
glass  tubes  are  full  of  water. 

By  applying  the  lips  to  the  outer  end  of 
the  tube  r  water  can  be  "  drawn  "  into  the 
mouth.  Can  this  be  done  when  the  tube 
b  is  closed  by  a  finger  at  the  top  ? 


Fig.  17. 


EXERCISE    1  1. 
SPECIFIC  GRAVITY  BY  FLOTATION  METHOD. 

Apparatus :  The  gallon  jar  (No.  10)  nearly  filled  with  water.  A 
slender  wooden  cylinder  (No.  13).  A  support  for  holding  this 
cylinder  upright  in  water  (No.  14).     A  measuring-stick  (No.  3). 

If  a  cylinder  floated  upright  with  its  top  just  level  with  the  top 
of  the  water,  we  should  at  once  know  its  specific  gravity  to  be  1. 
If  it  floated  just  half  in  and  half  out  of  water,  we  should  know 
its  specific  gravity  to  be  0.5.  The  cylinder  that  we  have  to 
use  will  not  float  all  in  water  or  exactly  half  in  water,  but 
if  we  float  it,  and  find  the  length  of  the  part  then  in  the  water, 
we  shall,  by  comparing  this  with  the  length  of  the  whole  cylin- 
der, find  some  way  of  ascertaining  the  specific  gravity  of  the 
cylinder. 

Measure  the  length  of  the  whole  cylinder. 

Float  the  cylinder  in  the  jar  (Fig.  18),  keeping  it  upright  by 
means  of  the  holder,  which  is  attached  to  the  side  of  the  jar. 
Joggle  the  cylinder  to  make  sure  that  it  is  free  to  take  its 
proper  position.     After   each   joggling  it   should  come    to   rest 


30 


PHTStCAL  EXPERIMENTS. 


at  the  same  depth  as  before.    The  rings  of  the  holder  must  not 

grip  the  cyhnder  at  all.  When 
sure  that  the  cylinder  is  float- 
ing as  it  should,  measure  the 
length  of  the  submerged  part, 
from  the  bottom  of  the  cylin- 
der up  to  the  flat  surface  of  the 
vrater,  not  to  the  top  of  the 
curve  where  the  svurface  meets 
the  glass  cylinder  wall. 

To  find  the  specific  gravity 
firom  the  two  measiu-ements 
now^  made,  begin  by  recalling 
the  fact  (see  Exercise  8)  that 
the  ■water  displaced  by  the 
floating  cylinder  vreighs  just 
as  much  as  the  cylinder  it- 
self. 

How  many  times  is  the  length 
of  the  submerged  part  of  the 
cylinder  contained  in  the  whole 
length  ? 

How  many  times  the  weight 
of  the  cylinder  would  be  tne 
weight  of  a  like  cylinder  of 
water  ? 

What,  then,  is  the  specific 
gravity  of  the  wooden  cylin- 
der? 


FiQ.  18. 


Suggestions  for  the  Lecture-room. 

PROBLEMS. 

(1)  A  block  whose  specific  gravity  is  0.6  floats  in  water. 
How  much  of  it  is  below  the  surface  ? 

(2)  A  block  whose  volume  is  1000  cu.  cm.,  and  whose 
specific  gravity  is  0.4,  floats  in  water.  How  many  cu.  cm. 
of  the  block  are  below  the  surface  ? 

(3)  A  block  that  weighs  4  oz.  in  air  is  fastened  to  a 


DENSITY  AND  SPECIFIC  GRAVITY. 


31 


sinker  that  weighs  6  oz.  in  water,  and  the  two  together 
weigh  3  oz.  in  water.  What  is  the  specific  gravity  of  the 
block  ? 

(4)  A  block  whose  specific  gravity  is  0.5,  and  which 
weighs  100  gm.  alone  in  air,  is  fastened  to  a  sinker  that 
weighs  150  gm.  alone  in  water.  How  much  will  both 
together  weigh  in  water  ? 

(5)  A  certain  body  has  the  density  187.2  in  pound  and 
foot  units.     What  is  its  specific  gravity  ? 


fr^ 


^ 


EXPERIMENTS. 

Take  two  glass  tubes,  each  about  6  in.  long,  connected 
by  a  rubber  tube  about  1  ft.  long.  Fill  the  whole  with 
water,  then  close  each  end  with 
a  finger.  Hold  one  end  beneath 
tlie  surface  of  tlie  water  in  the 
gallon  jar  (Fig.  19);  remove  the 
finger  from  that  end,  and  bring 
the  other  end,  still  closed,  down 
outside  the  jar  to  a  level  lower 
than  the  water  surface. 

Is  the  water  pressure  against 
the  finger  that  closes  the  tube 
now  greater  or  less  than  the 
atmospheric  pressure  upon  an 
equally  large  surface  ?  If 
greater,  the  water  will  run  out 
when  the  finger  is  removed.  If 
less,  the  air  will  run  in  and  drive  the  water  up  in  the 
tube  when  the  finger  is  removed.     Try  the  experiment. 

Repeat  the  experiment,  but  now  hold  the  outer  end  of 
the  tube,  before  opening  it,  higher  than  the  level  of  the 
water  in  the  jar. 

A  device  like  this,  which  is  found  in  a  great  variety  of 
forms,  is  called  a  siphon. 


Fig.  19. 


32 


PHtSTCA  L  EXPEtttMEN  TS. 


Show  in  operation  glass  models  of  "lifting-pump"  (App. 
No.  IX.,  Fig.  20)  and  force-pump  (App.  No.  X.,  Fig.  21), 
discussing  their  action. 


o 


t] 


[ 


V 


I 


Fig.  20. 


Fig.  21. 


EXERCISE    12. 

SPECIFIC  GRAVITY  OF  A  LIQUID:  TWO  METHODS. 

Apparatus:  The  gallon  jar  (No.  10)  nearly  filled  with  water, 
and  the  smaller  jar  (No.  15)  nearly  filled  with  a  solution  of  sul- 
phate of  copper.*  The  small  glass  bottle  (No.  16).  The  spring- 
balance  (No.  7).     Thiead. 


♦  This  sohition  may  be  made  by  puttiug  2  lbs.  of  sulpliate  of  cop- 
per crystals  into  about  3  qts.  of  warm  water  in  a  glass  vessel  aud  stir- 
ring occasioually  till  the  crystals  are  dissolved. 


DENSITY  AND  SPECIFIC  ORAVITT.  33 

First  Method. 

Weigh  the  bottle  empty.  Dip  the  bottle  into  the  jar  of  sulphate 
of  copper  and  let  it  fill  with  the  liquid.  Holding  the  bottle  over 
the  jar,  put  the  stopper  in  place,  thus  croTvding  out  the  excess  of 
liquid,  then  wipe  the  outside  of  the  bottle  and  w^eigh  it  carefiolly 
with  its  contents. 

Pour  the  sulphate  of  copper  back  into  its  jar,  then  fill  the  bottle 
with  water,  just  as  it  w^as  before  filled  with  the  other  liquid,  and 
again  weigh  the  bottle  and  its  contents. 

From  the  three  w^eighings  now  made  the  specific  gravity  of 
sulphate  of  copper  can  easily  be  found. 

Second  Method. 

We  found  in  Exercise  7  that  a  body  going  from  air  into  w^ater 
lost  in  apparent  weight  an  amount  equal  to  the  weight  of  its  own 
bulk  of  Txrater.  So  a  body  going  from  air  into  a  solution  of  sulphate 
of  copper  will  lose  in  apparent  w^eight  an  amovmt  equal  to  the 
weight  of  its  own  bulk  of  the  solution.  This  gives  a  method  of 
finding  the  specific  gravity  of  the  solution.  As  a  body  to  be  w^eighed 
first  in  air,  then  in  water,  then  in  the  solution,  we  will  use  the 
bottle  writh  enough  water  in  it  to  make  it  sink  in  either  liquid.  We 
may,  indeed,  use  the  bottle  full  of  Water,  just  as  it  was  left  at  the 
end  of  the  first  part  of  this  Exercise. 

Suggestions  for  the  Lecture-room. 

PROBLEMS. 

1.  A  glass  sphere  which  weighs  100  gm.  in  air  weighs 
60  gm.  in  water  and  40  gm.  in  sulphuric  acid  of  a  certain 
strength.     What  is  the  specific  gravity  of  the  glass  ? 

What  is  the  specific  gravity  of  the  sulphuric  acid  ? 

3.  A  vessel  contains  a  layer  of  water  10  cm.  deep  and 
above  this  a  layer  of  kerosene  (sp.  gr.  0.8),  10  cm.  deep. 
What  is  the  weight  of  a  cube,  each  edge  of  which  is  10 
cm.  long,  that,  if  placed  in  this  vessel,  will  sink  till  one 
half  its  volume  is  in  the  water  and  one  half  in  the  kero- 
sene ?  Ans.  900  gm.  What  is  its  specific  gravity  ?  Ans. 
0.9. 


34 


PHYSICAL  EXPERIMENTS. 


EXPERIMENTS. 

Exhibit  and  show  in  operation  two  graduated  glass  hy- 
drometers— one  for  determining  the  specific  gravity  of 
liquids  less  dense  than  water  (App.  No.  XI.),  the  other  for 
use  with  liquids  more  dense  than  water  (App.  No.  XII.). 

Show  in  a  bottle  together  several  liquids  of  different  spe- 
cific gravities  that  do  not  tend  to  mix  with  each  other;  for 
instance,  mercury,  chloroform,  water,  and  kerosene. 

Take  a  small  tumbler  containing  some  mercury  and 
drop  into  it  a  piece  of  iron. 

Take  a  bent  glass  tube  (App.  No.  XIII.,  Fig.  22)  each 
arm  of  which  is  about  one  foot  long  and  pour  water  into  it 


Fig.  22.  Fig.  28. 

till  both  arms  are  about  half  full,  then  pour  kerosene  into 
one  arm  till  it  is  nearly  full.  Does  the  water  now  stand 
as  high  in  the  other  arm  as  the  kerosene  does  in  the  first 
arm  ?  Can  you  from  this  experiment  see  a  third  method 
for  finding  the  specific  gravity  of  a  liquid  ? 


DEN8ITT  AND  SPECIFIC  ORA  VITT.  35 

Take  a  lead  Y-tube  and  connect  with  two  of  the  branches, 
by  means  of  short  rubber  tubes,  straight  glass  tubes  about 
one  foot  long  (App.  No.  XIV.,  Fig.  23).  Attach  to  the 
third  branch  of  the  Y-tube  a  somewhat  longer  rubber  tube, 
and  let  one  glass  tube  stand  in  a  vessel  of  water,  the  other  in 
a  vessel  of  kerosene  or  sulphate  of  copper.  Apply  the  lips 
to  the  rubber  tube  t  and  draw  out  some  of  the  air,  taking 
care  not  to  draw  any  liquid  into  the  mouth.  Note  the 
height  to  which  each  liquid  rises.  Does  this  experiment 
suggest  a  method  of  finding  the  specific  gravity  of  liquids  ? 


36  PHYSICAL  EXPERIMENTS. 


CHAPTER  III. 

THE  LEVER. 

Civilized  men  do  most  of  their  work  with  tools  or 
machines.  Many  tools  and  many  parts  of  machines  con- 
sist of  a  piece  of  iron  or  wood  or  other  material  movable  to 
a  certain  extent  upon  a  support  called  a  pivot,  or  axis,  or 
fulcrum,  by  means  of  which  a  force  applied  in  one  direction 
at  a  certain  spot  may  produce  another  force  different  in 
direction  or  in  magnitude,  or  in  both,  at  another  spot.  Such 
a  tool  or  part  of  a  machine  is  called  a  lever.  One  of  the 
most  familiar  examples  is  a  crowbar.  A  hammer,  as  used 
to  draw  out  a  nail  from  a  board,  is  another  example.  Each 
half  of  a  pair  of  scissors  is  a  lever.  We  shall  study  some 
very  simple  forms  of  the  lever  to  find  out  what  relations 
hold  between  the  forces  exerted  at  different  points. 

EXERCISE    13. 

THE  STRAIGHT  LEVER. 

Apparatus:  The  lever  and  supporting  bar  (No.  17)  fastened  to 
the  long  horizontal  bar  that  reaches  above  the  table  from  end 
to  end.  Two  scale-pans  (Nos.  18a  and  18b).  A  set  of  weights 
(No.  19). 

Hang  one  scale-pan  carrying  a  load  of  8  oz.  on  the  right-hand 
end  of  the  lever  at  a  distance  of  14  cm.  from  the  middle,  as  in  Fig. 
24. 

Hang  the  other  pan,  with  an  equal  load,  on  the  left-hand  end  of 
the  lever,  at  such  a  distance  from  the  middle  that  the  lever  will 
balance,  that  is,  stay  horizontal  when  once  placed  so,  even  when 
the  apparatus  is  jarred  somewhat  by  tapping  the  short  bar  to 
which  the  lever  is  attached.    Then  mahe  a  record  like  this : 

T«»ffwt  Left  (list.  Ritrht  wf  Right  dist. 

^®"^"^-  fr.  centre.  Kigbtwt.  fr.  centre. 

(1  4-  8)  =  9  oz (1  4-  8)  =  9  oz.  14.0  cm. 


THE  LEVER. 


37 


The  space  left  blank  here  is  to  be  filled  by  the  left-hand  distance 
which  the  pupil  finds  necessary  to  make  the  apparatus  balance. 

Change  the  right-hand  weight  to  7  oz.,  keeping  its  place  un- 
changed, and  move  the  left-hand  weight,  still  9  oz.,  to  some  new 
position  which  will  maike  the  whole  balance,  in  spite  of  jarring,  as 
before.  Make  a  record,  as  before,  of  the  weights  and  distances, 
putting  it  just  beneath  the  record  for  the  first  arrangement. 

Change  the  right-hand  weight  to  5  oz.  without  changing  its 
place  and  find  what  position  the  left-hand  weight,  still  remaining 
9  oz.,  must  have  in  order  that  the  lever  may  balance.    Record  the 


Fig.  24. 


distances  and  weights  for  this  case  under  the  records  already 
made  for  the  first  and  second  cases. 

One  more  case  may  be  taken  in  which  the  right-hand  weight 
becomes  3  oz.,  still  at  14  cm.,  which  will  give  a  fourth  line  in  the 
record  table.  More  observations  with  dififerent  arrangements 
might  be  made,  but  it  is  better  to  make  a  moderate  number  of 
good  observations  than  a  large  number  of  hasty  or  careless  ones. 

By  studying  the  record  table  now  made  the  pupil  may  find  a 
rule  by  which,  when  the  two  w^eights  and  one  distance  are  given, 
the  other  distance  may  be  found  by  calculation ;  or  when  the  two 
distances  and  one  weight  are  given  the  other  weight  may  be  found 
by  calculation. 


38 


PHYSICAL  EXPERIMENTS. 


®  @  ©  @ 


Fig.  25. 


Suggestions  for  the  Lecture-room. 

In  the  preceding  Exercise  the  class  found  out  how  to 
make  the  two  weights  hung  from  the  lever  balance  each 
other.  Let  us  ask  now  what  the  rule  for  balancing  would 
be,  if  there  were  more  than  two  weights  in  use,  as  in  Fig. 

25,   for    instance.      We    will 

make  the  apparatus   balance 

with  four  weights,  two  on  each 

side.     We  will  call  the  weight 

nearest  the  centre  on  the  left 

hand  weight  No.  1,  which  we 

will  write  TF, ,  for  short.    The 

other  weight  on  the  left-hand 

side  we  will  call  No.  3,  or  W^.     The  two  weights  on  the 

right  hand  we  will  call  IF,  and  TF,. 

When  the  whole  balances,  we  will  call 

the  distance  of  PF,  from  the  middle  Z), , 

((  t(  i(    VIT  ((  (I  ((  7) 

(t  tt  ((   pp"        «         ((  t(  r\ 

tt  (t  ((    "W"  t<  (t  K  T\ 

Now  if  we  go  back  for  a  moment  to  the  case  of  two 
weights,  which  the  class  has  studied,  and  if  we  call  these 
now  P,  and  P,,  and  their  distances  from  the  middle  d^  and 
d^ ,  we  can  state  the  rule  for  balancing  in  this  way  : 

P,  X  d^  must  equal  P,  X  d^. 

In  the  new  case,  where  we  have  four  weights,  we  may 
guess  that  the  rule  is 

(1^,  X  A)  +  (TT.  X  D,)  =  (IF,  X  Z)J  +  (^.  X  A), 

and  then  test  the  truth  of  our  guess  by  trial. 

Other  cases  may  be  tried  until  a  satisfactory  conclusion 
can  be  arrived  at. 


THE  LEVER.  39 

In  the  experiments  with  which  we  have  just  been  en- 
gaged the  weights  have  been  suspended  from  the  top  of  the 
lever  on  a  level  with  that  part  of  the  pivot  upon  which  the 
lever  rests.  In  other  experiments  which  are  to  follow  we 
shall  not  always  be  able  to  keep  this  arrangement,  and  we 
have  now  to  find  out  what  would  be  the  effect  of  hanging 
one  or  more  of  the  weights  from  points  higher  or  lower 
than  the  point  of  support  of  the  lever.  For  this  purpose 
we  shall  use  No.  XV.,  the  piece  of  apparatus  shown  in 
Fig.  26,  in  which  the  straight  lever  thus  far  used  is  re- 
placed by  a  circle  of  wood 
about  8  inches  in  diameter,  sup- 
ported by  a  screw  passing  hori- 
zontally through  the  centre. 
Such  a  circle,  or  disk,  of  wood 
comes  under  the  general  defi" 
nition  of  a  lever. 

We  will  hang  at  b  and  /  such 
weights  as  will    balance  each 
other,  leaving  the  disk  in  equi- 
librium, and  will  then  move  one  ^'**-  ^^■ 
of  the  weights  to  a  point  vertically  above  or  vertically 
below  its  present  place;  that  is,  from /to  e  or  g,  or  from  h 
to  a  or  c.     Shall  we  still  have  equilibrium  ? 

We  will  now  turn  the  disk  a  little,  so  that  the  lines  ah  c 
and  e  f  g  will  be  no  longer  quite  vertical,  and  will  see 
whether  now  a  weight  at  e  or  at  ^  has  just  the  same  effect 
as  if  at  /. 

A  careful  note  should  be  made  of  the  conclusions  ar- 
rived at,  for  future  use. 

In  the  experiments  upon  the  lever  thus  far,  the  lever 
itself,  whether  a  bar  or  a  disk,  has  balanced,  when  left  to 
itself  without  load.  We  have,  therefore,  not  had  to  con- 
sider the  weight  of  the  lever  itself.     But  many  levers  ar^ 


40 


PHYSICAL  EXPERIMENTS. 


used  in  such  a  way  that  their  own  weight  helps  or  hinders 
the  operation  to  be  performed  with  them.  To  understand 
such  cases  we  must  learn  something  about  what  is  called 
the  centre  of  gravity  of  a  body. 


EXPERIMENT. 


Take  a  board,  cut  in  any  irregular  shape,  like  Fig.  27, 
for  instance.    Make  several  small  holes  straight  through 


Fio.  27. 

the  board,  and  put  into  each  hole  a  wire  nail  that 
will  fit  close,  long  enough  to  project  about  half  an  inch 
on  each  side  of  the  board.  Tie  a  bullet  at  one  end  of  a 
thread  and  make  a  loop  in  the  other  end. 
Put  this  loop  over  one  liook  of  a  piece  of  wire 
bent  into  the  shape  shown  in  Fig.  28,  and  then 
rest  the  nail  a.  Fig.  27,  in  the  hooks  of  the  same 
wire,  so  that  the  board  and  the  string  carrying 
the  bullet  will  both  hang  free,  the  string  near  the  face  of 
the  board.     (The  whole  apparatus  as  shown  in  Fig.  27  will 


Fig.   28. 


THE  LEVER.  41 

be  called  No.  XVI.)  Mark  with  a  pencil  the  course  of  the 
string  downward  across  the  board. 

Then  suspend  the  board  by  the  nail  h  and  mark  the  new 
course  of  the  string.  Proceed  in  this  way  with  all  the 
nails  and  note  the  point  where  the  various  pencil-marks 
cross  each  other. 

Finally,  place  the  board  horizontal  and  balance  it  upon 
the  flat  head  of  a  lead-pencil,  noting  how  near  the  head  of 
the  pencil  comes  to  the  crossing  of  the  lines  marked  on 
the  board. 

By  such  experiments  as  this  we  come  to  see  that  there  is 
within  the  board  a  certain  point  which  always  hung  just 
beneath  the  support  when  the  board  came  to  rest  sus- 
pended from  any  one  of  the  nails.  We  see  that  the  same 
point  has  to  be  just  above  the  support  when  the  board  rests 
upon  the  pencil-top.  In  short,  the  board  acts  in  these 
experiments  as  it  would  if  all  its  weight  were  concentrated 
at  this  particular  point.  This  point  might  be  called  the 
centre  of  weight  or  centre  of  heaviness  of  the  board,  but 
it  is  commonly  called  the  centre  of  gravity. 

The  following  exercise  is  intended  to  make  the  pupil 
more  familiar  with  the  idea  of  centre  of  gravity,  and  to 
show  how  it  may  be  taken  account  of  in  the  use  of  the  lever. 

EXERCISE  14. 

CENTRE  OF  GRAVITY  AND  WEIGHT  OF  A  LEVER. 

Apparatus:  The  lever  of  No.  17,  detached  from  its  supporting 
bar,  and  a  small  block  (No.  20),  the  two  being  fastened  together, 
as  in  Fig.  29,  so  as  to  make  one  body,  which  will  be  called  the 


Fio.  29. 


lever  in  this  exercise.  A  slender  wooden  cylinder  (No.  13). 
1-oz.  scale-pan  (18a  or  18b).    A  1-oz.  wt.  from  No.  19, 


XL 


42  PHYSICAL  EXPERIMENTS. 

To  find  the  centre  of  gravity  of  the  lever,  balance  it,  bar  and 
block  fastened  together,  as  nearly  as  you  can  in  a  horizontal 
position  on  the  cylinder  laid  on  the  table  (see  Fig.  29),  the 
cylinder  being  kept  at  right  angles  writh  the  lever.  Find  in  this 
way  at  what  particular  mark  of  the  bar  the  centre  of  gravity  is, 
and  record  this  mark — for  instance,  9.1  cm. 

Then  suspend  the  1-oz.  scale-pan  carrying  a  1-oz.  wt.,  two  oz. 
in  all,  from  any  convenient  point  near  the  free  end  of  the  bar,  and 
letting  this  end  project  beyond  the  edge  of  the  table-top,  balance 
the  w^hole,  as  now  arranged,  as  nearly  as  you  can,  on  the  cylinder 
laid  on  the  table  as  before  (see  Fig.  30). 

Now  record  the  mark  from 
which  the  scale-pan  hangs,  33.4 
cm.,  we  may  suppose,  and  the 
mark  which  is  just  over  the  mid- 
dle of  the  cylinder  when  the 
whole  balances,  21.6  cm.,  let  us 
say. 
This  case  is  like  that  of  the 
Fig.  30.  lever  studied  in  Exercise  13.  The 

cylinder  now  taking  the  place  of  the  screw  as  a  support,  we  see 
that 

the  left-hand  weight  is  2  oz., 
«      «      "      distance  is  33.4  -  21.6  =  11.8  cm., 
"  right-hand  w^eight  is  the  w^eight  of  the  lever, 
"      «        "     distance  is  21.6  -  9.1  =  12.5  cm., 

that  is,  the  distance  from  the  support  in  Fig.  30  to  the  centre  of 
gravity  of  the  bar  and  block. 

We  do  not  as  yet  kno'w  the  w^eight  of  the  lever,  but  we  w^ill 
call  it  Wi ,  and  see  whether  we  can  find  its  amount  by  calculation. 
If  we  apply  the  same  rule  that  was  found  to  hold  true  in  Exercise 
13,  we  shall  have 

2xll.8  =  F,  X12.5, 
which  gives  for  the  weight  of  the  bar  and  block 

F,  =  ^  ^-V'^  =  1.89  oz.,  nearly. 

The  value  of  Wt  obtained  in  this  way  by  the  pupil  should  be 
compared  with  the  weight  of  the  bar  and  block  as  found  by  th? 


THE  LEVEE.  43 

teacher  with  some  balance,  e.g.  No.  XVII.,  much  more  sensitive 
than  the  spring-balance  used  by  the  class,  for  if  the  method  of 
this  Exercise  is  carefully  followed  it  will  give  the  weight  of 
the  lever  more  accurately  than  the  spring-balance  is  likely 
to  do. 

Suggestions  for  the  Lecture-room. 

In  connection  with  the  idea  of  centre  of  gravity  discuss 
and  illustrate  stable  equilibrium,  unstable  equilibrium,  and 
neutral  equilibrium  (see  any  ordinary  descriptive  text- 
book of  Physics). 

We  have  now  found  out  how  to  take  account  of  the 
weight  of  the  lever  itself,  when  we  need  to  do  so.  We 
know  that  all  its  weight  may  be  regarded  as  concentrated 
at  a  certain  point,  which  we  call  the  centre  of  gravity,  and 
we  have  tried  one  case  in  which  the  weight  of  the  lever 
itself,  acting  at  the  centre  of  gravity,  balanced  a  certain 
weight  suspended  from  the  bar.  In  common  levers,  like 
the  crowbar,  the  weight  of  the  bar  itself  may  be  very  im- 
portant sometimes,  when  the  fulcrum  is  a  long  distance 
from  the  centre  of  gravity  of  the  bar. 

We  will  now  return  for  the  present  to  cases  where  the 
centre  of  gravity  lies,  as  in  Exercise  13,  just  under  the 
point  of  support  of  the  bar.  In  this  case  the  weight  of 
the  lever  itself  does  not  tend  to  make  the  bar  tip  in  either 
direction  from  its  horizontal  position. 

Classes  of  Levers. 

In  the  levers  which  we  have  studied  thus  far  the  support, 
or  fulcrum  as  it  is  called,  lies  between  the  lines  of  suspen- 
sion of  the  two  weights.  This  kind  of  lever,  whether  it  is 
a  simple  bar  or  a  disk  or  an  object  of  irregular  shape, 
whether  its  centre  of  gravity  lies  at  the  point  of  support  or 
not,  is  called  a  lever  of  the  First  Class. 


44 


PHYSICAL  EXPERIMENTS. 


Fig.  31. 


To  take  a  simple  and  convenient  case  we  will  consider 

in  Fig.  31  a  circle  supported  at 
its  centre,  F.  We  will  suppose 
that  this  lever  is  used  for  the 
purpose  of  supporting  a  weight 
W,  and  the  force  used  for  this 
purpose,  whether  it  is  ajjplied 
by  means  of  another  weight,  as 
in  the  figure,  or  by  means  of 
the  hand,  or  in  any  other  way, 
we  will  call  the  Power. 

We  have  seen  in  the  experi- 
ments following  Exercise  13 
that,  as  the  lever  now  stands, 
it  makes  no  difference  whether 
W  is  suspended  from  the  point  which  now  carries  it  or 
from  some  point  higher  or  lower  in  the  same  vertical  line, 
which  is  called  the  line  of  action  of  W.  A  like  statement 
can  be  made  for  P.  We  shall  call  the  shortest  distance 
from  P's  line  of  action  to  the  fulcrum  the  poioer-arm,  and 
the  shortest  distance  from  PF's  line  of  action  to  the  fulcrum 
the  weight-arm. 

In  order  that  P  and  W  may  just  balance  each  other  we 
must  have,  as  can  be  seen  from  Exercise  13, 

poicer  X  power-arm  =  iveight  x  iveight-arm. 

This  is  the  laiu  for  a  lever  of  the  First  Class. 

But  we  may  have  a  case,  like  that  shown  in  Fig.  32,  in 
which  the  line  of  action  of  the  weight  lies  between  the  ful- 
crum and  the  line  of  action  of  the  power.  This  arrange- 
ment gives  us  what  is  called  a  lever  of  the  Second  Class. 

There  is  still  a  different  case,  shown  in  Fig.  33,  where  the 
line  of  action  of  the  power  lies  between  the  fulcrum 
and  the  line  of  action  of  the  weight.  This  is  called  a  lever 
of  the  Third  Class. 


TBB  LEVWR. 


46 


In  the  second  and  third  classes  of  levers,  as  in  the  first 
class,  the  shortest  distance  from  the  fulcrum  to  the  line  of 
action  of  the  weight  is  called  the  weight-arm,  and  the 


Fig.   32. 


Fig.  33. 


shortest  distance  from  the  fulcrum  to  the  line  of  action 
of  the  powe?'  is  called  the  poiuer-arm. 

The  pupil  is  to  find  out  by  means  of  the  following 
Exercise  whether  the  laws  of  the  second  and  third  classes 
of  levers  are  as  simple  as  the  law  of  the  first  class. 


EXERCISE     15. 
LEVERS  OF  THE  SECOND  AND   THIRD   CLASSES. 

Apparatus  :  The  lever  (No.  1 7)  supported  as  in  Exercise  1 3. 
A  scale-pan  (No.  18).  A  set  of  weights  (No.  19).  A  spring-balance 
(No.  7). 

Suspend  the  pan  with  a  load  of  8  oz.  at  a  point  5  cm.  from  the 
middle  of  the  lever,  and,  on  the  same  arm  of  the  lever,  at  a  dis- 
tance of  10  cm.  from  the  middle,  pull  upward  with  a  spring- 
bsdance,  connected  w^ith  the  lever  by  means  of  a  loop  of  thread, 
until  the  weight  is  balanced  and  the  lever  becomes  horizontal. 
Tou  have  here  a  lever  of  the  second  class.  Read  the  spring- 
balance  and  record  as  follow^s : 


46  PHYSICAL  EXPEUIMENTS. 

Lever  of  Second  Class. 

Weight.       Weight-arm.  Power.        Power-ai'm. 

9  oz.  5  cm.  ....  10  cm. 

Try  other  similar  cases,  and  study  them  all  until  you  are  able 
to  write  dovm  the  law  for  this  class  of  levers. 

Then  with  the  same  apparatus  place  the  spring-balance  between 
the  fulcrum  and  the  line  of  the  weight.  You  will  now  have  a 
lever  of  the  third  class.    Try  various  cases  and  record  aa  before. 

Lever  of  Third  Class. 
Weight.  Weight-arm.  Power.        Power-arm. 


Iiaw. 


Suggestions  for  the  Lecture-room. 

PROBLEMS. 

1.  A  lever  supported  at  its  centre  of  gravity  is  used  to 
lift  a  weight  of  100  lbs.  applied  at  a  distance  of  1  ft.  from 
the  fulcrum.  The  power  is  applied  5  ft.  from  the  fulcrum 
and  on  the  opposite  side  from  the  weight.  How  great 
must  the  power  be  ?  Must  the  power  be  applied  upward 
or  downward  ? 

2.  If  the  power  had  been  placed  on  the  same  side  of 
the  fulcrum  as  the  weight,  everything  else  being  as  de- 
scribed in  the  preceding  problem,  how  great  would  the 
power  have  to  be  ?  Would  it  be  applied  upward  or 
downward  ? 

3.  If  the  power  were  50  lbs.  applied  2  ft.  from  the  ful- 
crum toward  the  right,  and  if  the  weight  were  applied  8  ft. 
from  the  fulcrum  toward  the  right,  how  great  could  the 
weight  be  ? 

4.  If  a  weight  of  5  lbs.  were  placed  4  ft.  toward  the  right 
from  the  fulcrum,  and  a  weight  of  7  lbs.  6  ft.  toward 
the  right  from  the  fulcrum,  how  far  from  the  fulcrum 
toward  the  left  must  a  force  of  10  lbs.  be  applied  in  order 
to  make  the  whole  balance  ?  Ans.  6.2  ft. 


o 


THE  LEVER.  Al 

In  the  four  preceding  problems  the  weight  of  the 
lever  has  not  been  considered,  because  the  centre  of 
gravity  has  been  supposed  to  be  at  the  point  of  support. 
Suppose  now  that  the  lever  weighs  4  lbs.  and  that  its  centre 
of  gravity  is  3  ft.  to  the  right  from  the  fulcrum,  and  with 
this  new  condition  go  over  each  of  the  four  problems  again. 

If  we  take  a  case  like  that  shown  in  Fig.  34,  it  is 
plain   that   4   oz.  applied  7 

cm.  from  the  centre  will  bal-     ■ , 

ance  2  oz.  applied  14  cm. 
from  the  centre,  but  it  may 
not  be  perfectly  plain  how 
great  the  pull  on  the  ful- 
crum is  in  this  case.  We 
will,  therefore,  in  the  next 
Exercise  try  the  experiment  Fig.  34. 

in  one  or  two  simple  cases  and  see  what  the  result  will  be. 

EXERCISE   16. 

FORCE  EXERTED  AT  THE  FULCRUM   OF  A  LEVER. 

Apparatus:  The  lever  of  No.  17  freed  from  its  support.  Two 
scale-pans  (Nos.  18a  and  18b).  Two  1-oz.  wts.  and  one  2-oz. 
wt.  from  No.  19.  The  spring-balance  (No.  7).  A  piece  of  copper 
wire  about  I  mm.  in  diameter  bent  into  the  form  of  a  hook  {h  in 
Fig.  35).     A  piece  of  thread  about  6  inches  long. 

Suspend  the  bar  from  the  balance  in  the  manner  shown  by  Fig. 

35.     Note  and  record  the  w^eight 

of  the  bar   alone.     Then   suspend 

one  scale-pan  with  a  1  -oz.  weight 

from  one  arm  of  the  bar,  and  the 

other  scale-pan  with  a  2-oz.  weight 

from  the  other  arm  in  such  a  way 

as  to    balance,  taking  care  not  to 

~1    let    the    pans    and   weights    spill. 

Note    and    record  the   reading   of 

^'°-  ^-  the  balance.    Then  make  the  loads 

(pan  and  weight)  2  oz.  on  one  side  and  4  oz.  on  the  other,  and  read 


48  mraicAL  expertmbnts. 

and  record.  Try  any  other  experiments  that  you  can  with  the 
weights  furnished,  until  you  feel  reasonably  sure  that  you  know 
the  relation  between  the  weights  applied  and  the  pull  on  the 
balance.    Then  state  what  this  relation  is. 

Suggestions  for  the  Lediire-room. 

In  each  of  the  cases  in  Exercise  16  we  have  applied  two 
downward  forces  to  the  bar  in  suspending  the  two  scale- 
pans  with  their  loads,  and  have  found  these  two  forces  to 
be  balanced  by  another  force  exerted  upward  by  the 
spring-balance.  It  will  be  well  for  us  to  study  such  cases 
very  carefully,  for  similar  ones  are  often  found. 

Suppose  we  are  to  make  three  parallel  forces.  A,  B  and 
C,  just  balance  each  other  when  all  are  applied  to  the 
same  body.  Can  we  from  what  we  have  now  learned  tell 
anything  about  the  relative  magnitude  and  the  arrange- 
ment of  these  forces  ? 
We  know  that — 

1st.  All  the  forces  cannot  point  in  the  same  direction, 
^y.  Let  us  suppose  that  C  is  opposite  in  di- 

rection to  A  and  B. 

2d.  Tlie  force  G  must  he  equal  to  the 
sum  of  the  tioo  forces  A  and  B. 

%d.  llie  line  along  which  C  is  apjjlied 

must  lie  hetiveen  the  lines  along  tohich  A 

B>1  and  B  are  applied. 

^°-  ^-  Wi.  A  X  shortest  distance  from  line  of 

A  to  line  of  C  =  B  X  shortest  distance  from  line  of  B  to 

line  of  C.     (See  Fig.  36.) 

These  rules  apply  as  well  to  horizontal  forces  as  to  ver- 
tical forces.  Try  three  spriug-balances  laid  parallel  to  each 
other  on  a  table  and  pulling  at  some  light  horizontal  bar — 
a  lead-pencil,  for  instance. 

We  have  already  learned  to  consider  a  disk  pivoted  at 


r 


TBE  LEVER. 


49 


the  centre  as  a  kind  of  lever.    When  such  a  lever  is  worked 
by  means  of  strings   lying   upon  its   circumference   it  is 
called  a  pulley.     We  shall  now  see  that  the  pulley  form 
of  lever  has  some  great  advantages. 
Take  the  pulley  shown  in  Fig.  37  (No.  XV),  and  let  us 


Fig.  37. 


first  use  the  largest  circle  only.  If  we  fasten  two  equal 
weights,  W^  and  W^,  to  the  ends  of  a  string  and  pass  the 
string  across  the  top  of  the  pulley,  we  shall  of  course  find 
that  they  balance  each  other.  But  suppose  we  used  two 
strings,  one  for  TF,  and  the  other  for  W^ ,  fastening  each 
string  to  a  pin  or  tack  at  point  A,  but  letting  each  string 
rest  in  the  groove  of  the  pulley,  so  that  the  final  position 
of  the  two  strings  will  be  represented  by  Fig.  37.  Will  two 
equal  weights  balance  each  other  under  these  conditions  ? 
The  question  is  quickly  answered  by  trial,  and  by  turning 
the  pulley  a  little  one  way  or  the  other  one  may  try  the 
experiment  with  ^  in  a  variety  of  positions. 


50  PHYSICAL  EXPERiMENT8. 

Next  try  the  effect  of  a  horizontal  i^iill,  P,  applied  by  a 
spring-balance  at  the  top  of  the  pulley  to  balance  a  weight, 


Fig.  38. 


W,  see  Fig.  38.  (Remember  that  in  this  position  the  read- 
ing of  the  ordinary  8-oz.  balance  is  about  |  oz.  less  than 
the  real  force  exerted  by  it,  because  the  spring  of  the  balance 
does  not  now  support  the  weight  of  the  hook  and  bar, 
which  is  about  ^  oz.).  Find  by  experiment  whether  the 
force  P  must  be  greater  or  less  than,  or  equal  to,  the  direct 
pull  of  the  weight  W, 

Various  experiments  interesting  to  a  class  can  be  made 
by  balancing  a  weight  on  one  circle  of  the  pulley  by  a 
weight  on  another  circle,  and  the  simple  rule  which  holds 
for  the  relation  between  the  balancing  weights  is  easily 
made  out. 

We  see  that  the  advantage  of  a  pulley  like  this,  as  com- 
pared with  a  simple  bar  lever,  is  that  the  pulley  enables  us 
to  vary  the  direction  of  our  power  at  will  and  to  lift  a 
weight  a   much   greater  distance   than  we   could  with  a 


THE  LEVER. 


61 


bar  lever  no  longer  than  the  diameter  of  the  pulley.  lu 
fact,  the  distance  through  which  we  can  lift  the  weight  by 
means  of  the  pulley  depends  merely  upon  the  length  of 
the  string  that  supports  the  weight. 


But  we  can  do  more  with  a  pulley  than  we  have  yet  done. 
Let  us  take  now  a  well-made  small  metal  pulley  (No. 
XVIII),  such  as  one  may  get  at  a  hardware 
store,  and  arrange  it  according  to  the  indi- 
cations of  Fig.  39,  P  being  the  pulley,  M 
a  weight  suspended  from  an  axis  through 
the  centre  of  the  pulley,  B  a  spring- 
balance,  and  h  a  hook  to  which  one  end 
of  the  string  passing  beneath  the  pulley  is 
attached. 

To  what  class  of  levers  does  the  pulley  in 
this  position  belong  ?  What,  then,  should 
be  the  relation  between  the  weight,  which 
is  M  ijlus  the  weight  of  the  pulley  itself, 
and  the  pull  exerted  by  the  spring-balance  ? 
Find  by  experiment  whether  the  conclusion  reached  is 
correct.  (In  making  this  trial  one  must  remember  that 
friction  is  often  large  in  cheap  pulleys,  even  when  they 
are  well  oiled,  as  this  one  should  be.  Now  when  the 
load  is  being  steadily  raised,  the  hand  carrying  the  spring- 
balance  must  lift  harder  than  it  would  if  there  were  no 
friction,  but  when  the  load  is  being  steadily  lowered, 
the  hand,  pulling  just  hard  enough  to  prevent  the  load 
from  liurrijing^  is  assisted  by  the  friction.  The  mean 
between  the  reading  of  the  balance  going  up  and  the 
reading  of  the  balance  coming  down  will  show,  very 
nearly,  what  the  pull  required  to  sustain  the  load  would 
be  if  there  were  no  friction.) 


Fio.  39. 


Jjet  us  now  try  an  arrangement  like  that  shown  in 


52 


PHYSICAL  EXPERIMENTS. 


Fig.  40,  in  which  we  have  one  pulley,  A,  hooked  to  a 
bar  overhead  and  a  double  pulley,  B,  which 
moves  up  and  down  with  the  load  (No. 
XIX)  M.  Let  us  consider  what  should  be 
the  relation  between  the  pull  P  and  the 
weight  W,  which  is  M plus  the  weight  of  B, 
in  this  case. 

In  the  case  tried  just  before  we  had  two 
strings  holding  up  the  pulley  P.  We  have 
now  four  strings  holding  up  the  pulley  B. 
After  thinking  upon  the  matter  for  a 
little  time,  trying  to  study  out  what  is  the 
relation  between  P  and  W  with  this  ar- 
\B  rangement,  let  us  try  the  experiment  as 
we  have  already  tried  it  in  the  simple 
case,  noting  the  force  shown  by  the  spring- 
balance  when  M  is  moving  steadily  up  and 
again  when  it  is  moving  steadily  down, 
and  taking  the  mean  between  these  two 
forces  as  the  one  that  would  be  required 
to  balance  the  weight,  W,  if  there  were  no 
friction. 


M 


Fig.  40. 


Can  the  class  name  any  tools  or  machines,  not  already 
mentioned  in  this  book,  in  which  levers  or  pulleys  are 
used? 


THREE  FORCES  WORKING  THROUGH  ONE  POINT.  53 


CHAPTER   IV. 
THREE  FORCES  WORKING  THROUGH  ONE  POINT. 

In  studying  the  lever  we  have  usually,  though  not 
always,  had  parallel  forces  to  deal  with,  forces  acting 
straight  up  or  straight  down.  But  very  often  we  have  to 
do  with  bodies  that  are  acted  upon  by  forces  not  parallel 
to  each  other.  Thus  when  a  ladder  standing  upon  the 
ground  leans  against  a  house,  we  have  at  least  three  forces 
acting  upon  the  ladder:  1st,  the  earth's  attraction,  or, 
as  we  call  it  often,  the  loeight  of  the  body,  which  acts  as 
if  the  whole  substance  were  at  the  centre  of  gravity  ;  2d, 
the  push  of  the  ground  against  the  foot  of  the  ladder, 
which  push  is  not  straight  upward  ;  3d,  the  push  of  the 
wall  against  the  top  of  the  ladder. 

Again,  a  flying  kite  is  acted  upon  by  the  earth's  pull, 
straight  downward  ;  by  the  force  exerted  by  the  air,  which 
force,  because  of  the  wind,  is  not  straight  upward  ;  by  the 
pull  of  the  string,  which  pull  is  not  straight  downward. 

The  way  to  begin  the  study  of  such  cases  is  to  study  the 
case  of  three  forces  all  acting  straight  from  or  straight 
toward  a  single  point.  We  shall  take  such  a  case  in 
Exercise  17. 

EXERCISE    17. 

THREE    FORCES   IN  ONE    PLANE   AND    ALL  APPLIED    TO    ONE 

POINT. 

Apparatus  :  Three  8-oz.  spring-balances,  each  provided  with 

two  small  blocks  (No.  21)  to  go  under  its  sides  and  hold  it  flat  on 
its  back  w^hen  it  is  lying  upon  the  table.  The  rectangular  block 
(No.  9).     The  measvuring-stick  (No.  3).    A  sheet  of  paper.   Thread, 


54 


PHYSICAL  EXPERIMENTS. 


Take  two  pieces  of  strong  thread,  one  about  12  inches,  the 
other  about  6  inches,  long,  and  tie  one  end  of  the  short  thread  to 
the  middle  of  the  long  one.  Fasten  the  three  loose  ends  to  the 
hooks  of  the  spring-balances,  then  lay  the  latter  upon  the  table, 
putting  the  blocks  under  their  sides,  as  in  Fig.  41,  and  let  one  stu- 
dent pull  at  each  balance,  taking  care  that  the  slit  of  each  balance- 
face  is  in  a  straight  line  vrith  the  thread,  until  no  one  of  these  reads 
less  than  3  oz.     It  will  be  found  that  any  variation  in  the  angles 


8-oz.  Spring-balances. 
FiQ.  41. 

which  the  strings  make  with  each  other  w^ill  require  a  change  in 
the  forces.  Evidently  there  is  some  connection  between  the  di- 
rections of  the  strings  and  the  forces  necessary  to  balance  each 
other.  The  object  of  this  exercise  is  to  make  out  what  this  con- 
nection is.  It  is  simple  and  easy  to  remember.  We  can  study  it 
best  if  w^e  put  under  the  threads  a  sheet  of  paper  and  draw  on  this 
paper,  just  under  each  thread,  a  pencil-mark  parallel  to  the  thread, 
and  thea  write  down  alongside  each  peucil-inark  the  force  in  th§ 


THREE  FORCES  WORKING  THROUGH  ONE  POINT.   55 

direction  of  that  line,  as  shown  by  the  spring-balance.  The  bal- 
ances must  be  held  very  still  while  these  lines  are  being  drawn 
and  must  be  read  before  any  change  occurs  in  the  direction  of  the 
lines.  (It  may  prove  best  to  fasten  the  ring  of  each  balance  to  a 
weight  heavy  enough  to  hold  the  balance  in  place,  thus  relieving 
the  pupils,  who  might  grow  tired  and  unsteady  in  holding  the 
balances  long  enough  to  permit  of  drawing  the  pencil-marks 
properly.)  To  draw  a  line,  place  one  side  of  the  block  (No.  9) 
close  alongside  one  branch  of  the  thread,  taking  care  not  to  push 
the  thread  out  of  place,  and  then  run  the  point  of  a  well-sharp- 
ened pencil  along  the  edge  of  the  block  under  the  thread.  Draw 
the  other  lines  in  the  same  way,  doing  it  all  very  carefully. 
Each  pupil  in  turn  makes  a  set  of  lines,  and  records  alongside 


Fig.  43. 


them  the  proper  forces.  The  directions  of  the  pulls  should  be 
varied  somew^hat  by  each  pupil,  in  order  that  his  lines  and  forces 
may  not  be  exactly  like  those  of  other  pupils. 

Take  now  the  w^ooden  ruler  (No.  3),  and  extend  the  three  lines 
toward  each  other  till  they  meet  at  one  point.  This  they  will  do 
if  they  have  been  drawn  originally  just  under  the  threads.  If  they 
do  not  all  meet  in  one  point,  a  new^  line  should  be  draw^n  parallel 
to  one  of  them,  w^hich  new^  line  will  pass  through  the  crossing  of 
the  other  two  lines,  and  this  new  line,  the  dotted  line  in  Fig.  42, 
is  then  to  be  used  in  place  of  the  original  line.  The  three  lines  as 
now  drawn  -will  represent  accurately  the  directions  of  the  three 
forces. 

Now  measure  off  from  the  common  point  along  the  line  A  a 
distance  of  \  cm.  for  e^ch  ounce  (or  each  30  gm.,  if  the  forces  ar€ 


56 


PHYSICAL  EXPERIMENTS. 


measured  in  grams)  of  the  force  'which  was  exerted  along  that  line, 
and  put  a  small  arrovr-head  (see  Fig.  42)  at  the  end  of  this  meas- 
ured distance.  Erase  that  part  of  line  A  which  lies  beyond  the 
arrow-head. 

Do  the  same  with  lines  B  and  0  that  has  been  done  wth  A. 
The  three  arrows  thus  obtained,  all  reaching  from  the  same  point, 
represent  the  magnitude  and  the  direction  of  the  three  forces 
exerted  by  the  spring-balances. 

Now  with  A  and  B  of  Fig.  42  as  two  of  the  sides  make  a  parallel- 
ogram, taking  pains  to  make  it  accurate.*  Then  make  a  paral- 
lelogram w^ith  B  and  C  as  sides ;  then  one  with  A  and  C  as  sides. 
Compeire  the  length  and  direction  of  the  line  C  with  the  length 
and  direction  of  the  diagonal  of  the  parallelogram  AB ;  the  line 
A  with  the  diagonal  of  the  parallelogram  BC ;  the  line  B  with 
the  diagonal  of  A  C. 

*One  line  may  be  drawn  very  nearly  parallel  to  another  by  means 
of  a  device  illustrated  by  Fig.  43.     LI  is  a  line  already  drawn.     The 


E 
/ 


Fig.  43. 


block  (No.  9)  is  so  placed  that  for  an  eye  placed  at  E  the  edge  mn 
appears  to  be  close  to  LI  and  parallel  to  it.  Then  a  pencil-mark  is 
made  along  the  edge  op. 

A  better  method  is  to  set  the  edge  op  on  the  Hue  Li  and  then  guide 
the  block  to  a  new  position  by  sliding  it  along  the  straight  edge  of 
9  ruler. 


THREE  FORCES  WORKING  THROUGH  ONE  POINT.   57 


Fio.  44. 


Prom  this  comparison  make  a  rule  showing  how  to  find  the 
direction   and  magnitude   of  a  force  C  which,  put 
with  two  forces  represented  by  the  lines  A  and  B 
(Fig.  44),  will  just  balance  them.  A.  \ 

Suggestio7is  for  the  Lecture-room. 

ProUem  for  the  class,  to  be  solved  by  simple 
cjilculation  or  by  drawing  a  iigure  and  meas- 
uring: A  force  of  7  lbs.  pulls  north  from  a 
certain  point  and  a  force  of  4  lbs.  pulls  east 
from  the  same  point.  How  large  must  a  third  force  be 
to  hold  them  in  check,  and  what  will  be  its  general  direc- 
tion ? 

The  Inclined  Plane. 

The  facts  learned  in  Exercise  17  will  enable  us  to  under- 
stand a  contrivance  very  often  used  for  raising  heavy 
weights.  You  have  all  seen  barrels  of  flour  or  other 
heavy  objects  loaded  upon  wagons  by  rolling  them  up  a 
plank  or  a  pair  of  rails,  placed  with  one  end  on  the  ground 
and  the  other  upon  the  wagon,  so  as  to  make  the  ascent 
gradual  instead  of  straight  up.  The  flat  slanting  surface 
up  which  the  body  is  rolled  is  called  an  Inclined  Plane. 

Sometimes  a  body  is  lifted  by  forcing  an  inclined  plane, 
the  slanting  face  of  a  wedge,  under  it,  as  in  Fig.  45. 


Fig.  45. 


Sometimes  the  force  used  by  an  experimenter  or  a  work- 
man with  the  inclined  plane  is  jDarallel  to  the  inclined  sur- 
face; sometimes  it  is  parallel  to  the  base-line  of  the  plane, 
the  horizontal  surface  of  a  wedge,  for  insta,nce,  in  Fig.  45, 


58 


PHYSICAL  EXPERIMENTS. 


It  is  well  known  that  the  force  required  to  move  a  body 
up  an  incline,  or  to  keep  it  from  sliding  down  the  incline, 
is  greater  the  greater  steepness  of  the  incline.  The  ex- 
periments now  to  be  undertaken  are  for  the  purpose  of 
making  out  the  connection  between  the  weight,  the  steep- 
ness of  the  incline,  and  the  power  required  to  hold  the 
weight  from  sliding  or  rolling  down  the  incline,  when 
there  is  no  friction  to  oppose  this  motion. 

We  shall  consider  first  the  case  in  which  the  power  is 
applied  parallel  to  the  inclined  surface. 

Take  apparatus  No.  XX  and  adjust  it  as  indicated  by 
Fig.  46,  putting  7  oz.  upon  the  pan,  so  that  P  =  7  -{-  1  = 
8  oz.     Then  raise  or  lower  the  incline  till  the  weight  W 


Fig.  46. 


will  barely  roll  up  the  incline  when  the  apparatus  is  pur- 
posely jarred  slightly.  (The  incline  cannot  be  quite  so 
steep  when  this  takes  place  as  it  might  be  if  there  were  no 
friction.  If  a  knot  is  made  in  the  thread  near  where  it 
passes  over  the  pulley  at  the  top  of  the  incline,  a  very 
slight  movement  up  or  down  the  incline  can  be  detected 
by  watching  the  position  of  this  knot.  A  slight  movement 
is  enough.  It  is  not  necessary  to  have  the  weight  IF  move 
far.) 


THREE  FORCtJS  WORKING  THROUGH  ONE  POINT.  ^9 

As  soon  as  this  adjustment  is  made,  read  H,  the  length 
of  the  vertical  scale  from  the  top  of  the  base-board  to  the 
under  side  of  the  incline,  and  record  in  the  way  indicated 
in  the  table  below  (upper  row  of  numbers). 

Then  without  changing  P  raise  the  incline  somewhat 
more,  until  W  will,  when  the  apparatus  is  jarred,  barely 
roll  down  the  incline.  (The  incline  must  be  somewhat 
steeper  for  this  than  it  would  have  to  be  if  there  were  no 
friction.)  When  the  proper  adjustment  is  made  read  the 
new  value  of  H  and  record  it  in  the  second  line  of  the  table 
below. 

To  find  the  H  that  would  make  P  just  balance  W,  if 
there  were  no  friction,  take  the  mean  between  the  two 
values  now  recorded.  Then  find  the  L  that  would  corre- 
spond to  this  value  of  H,  L  being  the  distance  along  the 
inclined  scale  from  the  hinge  to  the  point  of  crossing  the 
vertical  scale. 

P  W  H  L 

Going  up 8  oz.       16  oz        

"      down....   8   "        16    « 

To  balance 8  oz.       16  oz (mean)     

Then  make  P  =  Q  oz.,  then  4  oz.,  and  in  each  case 
repeat  the  operations  just  described. 

Then  bring  together  the  results  of  all  the  observations 
in  the  following  form : 

P  W  H  L 

Kequired  to  balance  J  . . . .         ....         .... 

It  will  then,  probably,  be  easy  to  make  out  the  law  which 
holds  in  this  application  of  the  inclined  plane. 

For  experiments  in  which  the  power  is  applied  parallel 
to  the  base-line  we  cannot  make  use  of  a  string  running 


eo 


PHYSICAL  EXPERIMENTS. 


over  a  pulley.  We  must  apply  the  power  by  means  of 
the  spring-balance,  as  shown  in  Fig.  47,  the  long  slot  cut 
through  the  incline  lengthwise  allowing  us  to  do  so. 


Fig.  47. 

Find  by  trial  a  steepness  of  incline  that  will  make  P 
about  7  oz.,  and,  keeping  this  steepness  unchanged  for  the 
time,  find  how  large  P  is  when  it  is  pulling  W  slowly  and 
steadily  up  the  incline,  and  how  large  when  it  is  letting  W 
run  with  equal  slowness  and  steadiness  down  the  incline. 
Take  the  mean  of  these  two  values  as  the  one  that  would 
be  needed  to  balance  W  if  there  were  no  friction.  (The 
mean  of  the  two  values  of  P  is  not,  in  this  case,  exactly 
the  quantity  wanted,  because  the  greater  pull  of  P  when 
W  is  going  up  the  incline  makes  W  press  harder  against 
the  incline  when  going  up  than  when  going  down.  The 
mean  value  of  P,  as  now  found,  is  a  little  greater  than  the 
value  wanted,  but  so  little  that  the  error  is  not  important.) 

We  record,  then,  for  this  case : 


Going  up . . . 
"     down 


W 
16 

16 


H 


To  balance 


. . .  (mean)     16 


where  B  is  the  length  of  the  base-line  from  the  hinge  to 
the  foot  of  H. 


THREE  FORCES  WORKING  THROUGH  ONE  POINT.  61 

Lower  the  incline  and  try  various  degrees  of  steepness, 
so  that  P  will  be  in  one  case  about  5  oz.  and  in  another 
case  about  3  oz.  Then  arrange  the  results  of  the  various 
cases  tried  in  this  form : 

P  W  H  B 

Required  to  balance  } 

Look  for  the  law  here,  and  state  it  when  found. 

With  the  aid  of  a  little  knowledge  of  geometry  the  laws 
of  the  inclined  plane  might  be  found  without  these  ex- 
periments, from  the  law  of  the  parallelogram  of  forces. 
Fig.  48  suggests  the  reasoning  for  the  case  of  a  pull  paral- 


FiG.  48. 


lei  to  the  incline.  W  here  represents  the  weight  of  the 
body  exerted  straight  downward  from  the  centre  of  grav- 
ity. The  dotted  line  W  is  equal  to  W,  but  opposite  in 
direction.  It  is  the  diagonal  of  a  rectangle  having  N  and 
P  as  sides.  iV" represents  the  force  exerted  upon  the  roller 
by  the  plane  L,  a  force  which  is  straight  outward  from  the 
plane  L,  if  there  is  no  friction  (see  the  next  Exercise)  of 
the  roller  against  the  plane.    P  represents  the  pull,  parallel 


62 


PHYSICAL  EXPERIMENTS. 


to  the  plane  L,  which  with  the  force  N  will  just  balance 
W.  Compare  the  dotted  triangle  with  the  triangle  whose 
sides  are  L,  B,  and  H,  and  see  whether  you  can  by  use  of 
your  geometry  make  out  the  relation  between  P,  W  ( =  W) 
and  certain  sides  of  the  triangle  LBH. 

Fig.  49  suggests  the  reasoning  for  the  case  of  a  pull  par- 
allel to  the  base. 


FRICTION.  63 


CHAPTER  V. 
FRICTION. 

Whek  we  push  a  heavy  block  along  on  the  top  of  a 
table  we  feel  a  certain  resistance.  We  know  from  experi- 
ence that  by  making  the  surface  of  the  table  and  the  sur- 
face of  the  block  very  smooth  we  can  lessen  the  resistance. 
This  resistance,  the  amount  of  which  depends  upon  the 
condition  of  the  rubbing  surfaces,  is  called  Friction. 

Friction  always  opposes  motion,  whatever  may  be  the 
direction  of  the  motion.  That  is,  it  merely  tends  to  stop 
the  motion.  It  never  helps  to  push  the  block  hack  to  the 
position  where  it  started. 

We  shall  measure  in  a  number  of  cases  the  force  required 
to  keep  a  block  moving  steadily  along  on  a  sheet  of  paper 
laid  upon  a  level  table-top. 

EXERCISE   18. 
FRICTION  BETWEEN  SOLID  BODIES. 

Apparatus  :  A  spring-balance  (No.  7).  A  rectangular  block  (No. 
9).  Set  of  weights  (No.  1 9).  A  smooth  sheet  of  paper  about  1  ft. 
wide  and  1^  ft.  long.     Thread. 

We  shall  first  consider  the  velocity  of  the  motion.  That  is,  we 
shall  ask  whether  the  force  required  to  keep  up  a  slow  steady 
motion  is  greater  or  less  than  that  required  to  keep  up  a  more 
rapid  steady  motion. 

Lay  the  block  on  one  of  its  broad  sides,  and  attach  it  to  the 
spring-balance  by  a  thread  passing  around  but  not  under  the  block. 
Load  the  block  with  weights  until  the  force  required  (for  a  very 
slow,  steady  motion)  is  about  3  oz.  Draw  the  block  parallel  to  its 
grain  along  the  sheet  of  paper  several  times  with  a  very  slow, 


64  PHYSICAL  EXPERIMENTS. 

steady  motion,  and  several  times  with  an  equally  steady  motion 
two  or  three  times  as  fast.  As  the  paper  is  likely  to  grow^  some- 
'what  smoother  \inder  the  repeated  rubbing,  the  experimenter 
should  not  make  all  his  slow  trials  first,  but  should  change  from 
slow  to  fast  and  fast  to  slovr  a  number  of  times. 

Record  yoiir  conclusion  as  to  whether  the  slow  or  the  more 
rapid  motion  requires  the  greater  force. 

We  shall  next  try  to  find  out  w^hether,  the  total  weight  being 
the  same  as  before,  it  is  easier  or  harder  to  draw  the  block  on  a 
narrow  side  than  on  a  broad  side.  Use  the  same  block  and  the 
8<une  load  of  w^eights,  pulling  it  now  as  before  parallel  to  its  grain. 

Of  course  the  side  upon  which  the  block  slides  should  in  all 
cases  be  clean,  and  the  broad  and  narrow  sides  \7hich  are  com- 
psured  should  be,  as  nearly  as  practicable,  equally  smooth.  The 
thread  must  not  be  between  the  rubbing  surfaces  in  any  case. 

Record  your  conclusion  as  to  whether  the  broad  side  or  the 
narrow  side  offers  the  greater  resistance  to  the  motion. 

Finally,  we  shall  ask  w^hat  connection  there  is  between  the 
weight  draw^n  and  the  force  required  to  draw  it.  For  this  pur- 
-  pose  vary  the  weights  placed  upon  the  block,  using  not  less  than 
6  oz.  for  the  least  and  as  much  as  1 6  oz.  for  the  greatest  load. 

Add  to  the  load  in  each  case  the  weight  of  the  block  itself  and 
make  the  record  in  the  following  form,  TV  being  the  load  and  b 
the  weight  of  the  block : 

W-\-b.  F  (Force  required). 


liook  for  any  simple  relation  between  {W-\-b)  and  B. 

The  experiments  just  described  will  teach  a  number  of  useful 
facts  about  friction  between  two  solid  substances,  but  one  must 
be  careful  not  to  apply  the  conclusions  here  arrived  at  to  extreme 
cases,  extremely  slow  or  very  fast  motion,  for  instance ;  or  to  cases 
where  the  pressure  is  great  enough  and  the  edge  of  the  sliding 
body  narrow  enough  to  cause  an  actual  cutting  of  the  body  into 
the  surface  over  which  it  should  slide. 


THE  PENDULUM.  65 


CHAPTER   VI. 

THE    PENDULUM. 

Before  leaving  the  subject  of  Mechanics  and  going  to 
that  of  Light  it  is  well  to  learn  something  about  pendu- 
lums, which  are  used  to  control  the  motion  of  clocks. 

If  you  were  to  examine  the  works  of  an  old-fashioned 
clock  you  would  find  the  power  which  drives  it  in  a  heavy 
weight  working  upon  a  kind  of  pulley  by  means  of  a  long 
cord,  but  the  device  which  governs  the  speed  of  the  works 
and  allows  the  motion  to  be  neither  too  fast  nor  too  slow 
is  the  pendulum.  As  a  crowd  of  men  at  a  turnstile,  how- 
ever they  may  try  to  force  their  way,  can  pass  no  faster 
than  the  swinging  turnstile  permits,  so  the  clock-weight, 
which  if  the  control  were  removed  would  run  down  at 
once  with  a  furious  buzzing  of  the  wheels,  is  allowed  by  the 
pendulum  to  descend  only  very  slowly,  a  very  little  dis- 
tance at  every  swing  of  the  pendulum,  and  not  at  all  when 
the  pendulum  does  not  move. 

The  rate  at  which  the  clock-wheels  can  move,  then,  de- 
pends upon  the  length  of  time  required  for  each  swing  of 
the  pendulum.  We  will  try  a  few  simple  experiments  with 
very  simple  pendulums  to  find  out — 

1st.  How  does  the  time  required"  for  a  single  swing  de- 
pend upon  the  length,  or  loidth,  of  the  swing  ? 

For  this  purpose  we  have,  hanging  side  by  side,  two  pen- 
dulums of  equal  length,  Nos.  1  and  2  in  Fig.  50,  each  con- 
sisting of  a  bullet  suspended  by  a  silk  thread  about  3  feet 
long. 

(A  convenient  method  of  suspending  each  pendulum  is 


66 


PHYSICAL  SJ^PERlMmTB. 


shown  in  Fig.  51,  where  B  is  one  end  of  a  wooden  bar, 
which  is  bevelled  off  on  the  side  from  which  the  pendulum 
hangs.  C  is  a  cork  fastened  to  the  top  of  the  bar  and  hav- 
ing in  it  a  slit  made  by  a  sharp  knife,  through  which  slit 
the  silk  thread,  S,  passes.    If  this  part  of  the  thread  is 


Fig.  50. 


o 

Fig.  51. 


waxed,  the  fastening  thus  obtained  holds  the  pendulum 
securely,  although  it  is  very  easy  to  increase  or  decrease  the 
length  of  the  pendulum  at  will.  The  length  of  the  pen- 
dulum is  to  be  measured  from  the  under  side  of  the  bar  to 
the  centre  of  the  ball.  It  is  intended  that  the  length  of 
No.  3  in  Fig.  50  shall  be  one  fourth  that  of  No.  2,  and  the 
length  of  No.  4  one  niiith  that  of  No.  2.  It  is,  therefore, 
convenient  to  make  the  length  of  No.  2  just  36  inches, 
which  will  require  9  inches  for  the  length  of  No.  3,  and  4 
inches  for  that  of  No.  4.  The  suspended  body  is  a  bullet 
in  the  case  of  each  pendulum  except  No.  5,  where  it  is  some 
lighter  object — a  marble  for  instance.  No.  5  has  the  same 
length  as  No.  1.) 


THE  PENDULUM.  67 

The  five  pendulum  balls  and  the  bar  B,  prepared  for  re- 
ceiving the  threads,  will  together  be  called  No.  XXI. 

We  will  first  set  No.  1  and  No.  2  swinging  at  the  same 
instant  and  with  the  same  width,  or  length,  of  swing,  and 
watch  them  both  for  a  little  while  until  we  see  that  under 
these  circumstances  they  keep  together.  No.  1  taking  just 
as  long  a  time  for  one  swing,  or  for  any  number  of  swings, 
as  No.  2  does. 

Then  draw  the  ball  of  No.  1  about  one  inch  aside  from 
its  position  of  rest,  and  the  ball  of  No.  2  about  fifteen 
inches  aside  from  its  position  of  rest,  and  release  both  balls 
at  the  same  instant.  The  class  will  watch  the  two  for  some 
little  time,  a  quarter  of  a  minute  or  longer,  and  see  whether 
at  the  end  of  that  time  they  begin  each  swing  together,  as 
they  did  at  first.  If  they  do  not,  observe  which  one  has 
gained  upon  the  other,  and,  after  one  or  two  repetitions 
of  the  experiment,  write  down  an  answer  to  the  question 
which  the  experiment  was  intended  to  meet.  This  answer 
should  state  which  swing,  the  long  or  the  short,  if  either, 
takes  the  longer  time,  and  whether  the  difference  in 
time  is  large  or  small  compared  with  the  time  of  either 
swing. 

We  will  now  consider — 

(2)  How  does  the  time  required  for  a  single  swing  de- 
pend upon  the  length  of  the  pendulum,  from  the  support 
down  to  the  centre  of  the  ball  ? 

The  teacher,  holding  a  watch  in  his  hand,  draws  ball 
No.  2  several  inches  aside  from  its  position  of  rest  and, 
releasing  it  at  a  convenient  moment,  gives  a  signal  to  the 
class,  and  the  pupils  count  the  number  of  single  swings 
till,  at  the  end  of  20  seconds  from  the  start,  a  signal  is 
given  to  stop  counting. 

In  a  similar  manner  the  number  of  swings  of  No.  3  in 
20  seconds,  and  the  number  of  swings  of  No.  4  in  an  equal 


68  PHYSICAL  EXPERIMENTS. 

time,  are  found,  and  the  observations  for  the  three  pendu- 
lums are  recorded  in  a  table,  as  follows : 


Pendu- 
lum. 

No.  2 

Whole 
time. 

20  sec. 

Number 
of  swings. 

Time  of 
one  swing. 

Length 
of  pend. 

36 

Square  root 
of  length. 

6 

"    3 

t( 

...  J 

.... 

9 

3 

"    4 

« 

.... 

•  •  .  . 

4 

2 

The  numbers  to  fill  the  fourth  column  must  be  found 
from  those  in  the  second  and  third  columns.  A  compari- 
son of  the  fourth  column  with  the  sixth  column  will  prob- 
ably show  that  there  is  a  close  relation  between  the  time  of 
swing  and  the  length  of  a  pendulum. 

Finally,  a  comparison  of  No.  1  and  No.  5,  set  in  motion 
at  the  same  time  and  with  the  same  width  of  swing,  will 
show  whether  the  time  of  swing  depends  much  upon  the 
nature  of  the  suspended  body. 

It  will  doubtless  be  noticed  that  the  luidth  of  swing  of 
the  lighter  body  diminishes  more  rapidly  than  that  of  the 
heavier  one.  This  gradual  loss  of  motion  is  due  to  the 
resistance  of  the  air.  The  resistance  is  about  the  same  for 
both  bodies,  if  they  have  the  same  size,  shape,  and  velocity, 
but  a  light  body  is  more  quickly  stopped  by  a  given  re- 
sistance than  a  heavier  body.  This  is  the  reason  why  one 
cannot  throw  an  acorn  or  a  piece  of  cork  so  far  as  one 
can  a  stone  of  the  same  size. 

It  has  been  said  above  that  pendulums  are  used  to  con- 
trol clocks,  but  many  clocks  and  all  watches  are  controlled 
by  means  of  vibrating  springs  ;  for  these,  like  pendulums, 
are  very  regular  in  their  swings  and  so  are  good  time- 
keepers. The  controlling  springs  (see  the  "  balance  "  of  a 
watch)  must  not  be  confused  with  the  much  larger  driving 
springs,  or  "  maifi  springs,"  which  are  used  in  watches 
and  in  most  clocks  of  the  present  day. 


LIGHT.  69 


CHAPTER  VII. 
LIGHT. 

We  say  that  a  lamp  gives,  or  gives  out,  light.  This  is 
true.  Light  is  something  that  comes  to  our  eyes  from  any 
object  and  enables  us  to  see  the  object  from  which  the 
light  comes.  The  light  which  most  objects  send  to  our 
eyes  has  come  to  these  objects  directly  or  indirectly  from 
the  sun  or  from  a  lamp,  as  we  may  know  from  the  fact 
that  if  we  take  these  objects  into  a  dark  room,  where  no 
light  falls  upon  them,  they  do  not  send  any  light  to  our 
eyes,  and  so  we  do  not  see  them. 

Of  course  we  see  many  things  every  day  upon  which 
neither  the  sun  nor  any  lamp  is  directly  shining.  We  see 
them  by  what  is  called  "  daylight."  This,  however,  is 
sunlight,  although  it  may  not  have  come  straight  from 
the  sun  to  the  objects  that  we  see  lighted  up  by  it.  It 
may  have  gone  from  the  sun  to  a  mass  of  clouds,  from 
the  clouds  to  the  surface  of  fields  or  streets  or  walls  of 
houses,  and  from  such  surfaces  into  corners  where  the  sun 
itself  is  never  seen. 

Light  as  it  comes  from  the  sun,  or  from  most  lamps,  is 
of  many  different  kinds,  all  blended  together  so  that  the 
eye  does  not  distinguish  one  kind  from  another;  but  when 
this  mixture  of  lights  falls  upon  certain  objects,  pieces  of 
glass  called  prisms,  for  instance,  the  mixture  is  broken  up 
and  we  see  the  different  colors. 

EXPERIMENT. 

Hold  a  glass  prism  (No.  XXII)  in  the  direct  sunlight  in 
such  a  position  that  light  after  passing  through  the  prism 
will  fall  upon  a  white  surface  not  in  the  direct  sunlight, 


70  PHYSICAL  EXPERTMKNTS. 

Most  objects  upon  which  sunlight  falls  make  some 
change  in  it  by  destroying  (or,  rather,  changing  into  some- 
thing else)  some  parts  of  the  mixture,  so  that  the  light 
which  leaves  these  objects  and  comes  to  our  eyes  is  a  dif- 
ferent mixture  from  that  which  the  sun  sends  directly  to 
us,  and,  as  we  say,  has  a  different  color. 

Thus  the  light  which  comes  through  a  solution  of  sul- 
phate of  copper  is  blue,  because  the  sulphate  of  copper  has 
stopped  the  other  parts  of  the  light  which  entered  it  from 
passing  through.  The  sulphate  of  copper  has  added  noth- 
ing to  the  light.  It  has  merely  taken  away  a  certain  part 
of  it.  One  can  get  from  a  druggist  little  packages  of  dyes 
of  various  colors,  which,  when  dissolved  in  water,  give 
beautifully  colored  liquids.     (See  No.  XXIII.) 

When  we  speak  of  the  color  of  an  object  we  mean  the 
color  of  the  light  which  that  object  sends  to  our  eyes.  We 
distinguish  one  object  from  another  by  sight,  mainly 
by  difference  in  color,  but  partly  by  difference  in  bright- 
ness. 

An  object  which  allows  any  particular  kind  of  light  to 
pass  through  it  without  perceptible  loss  is  said  to  be 
transparent  to  that  kind  of  light.  If  it  allows  all  kinds  of 
light  to  pass  through  it  without  loss,  so  that  sunlight  suf- 
fers no  change  in  traversing  it,  the  object  is  said  to  be 
transparent  and  colorless.  Water  and  good  window-glass 
come  near  being  transparent  and  colorless. 

Most  objects  take  their  color  from  light  which  does  not 
appear  to  have  passed  through  them,  but  to  have  been 
reflected  from  their  surfaces.  It  is  known,  however,  that  in 
many  cases  this  light  really  has  penetrated  a  little  distance 
into  the  object  and  has  then  come  back,  so  that  we  really 
get  light  that  has  passed  through  a  thin  layer  of  the 
substance.  Light  which  is  reflected  from  the  outer 
surface  of  bodies  is  usually  not  changed  in  color  by  this 
reflection. 


LIGHT. 


71 


EXPERIMENT. 

Let  a  beam  of  bright  sunlight  fall  very  obliquely  upon 
a  deep-blue  solution 
of  sulphate  of  cop- 
per, Fig.  52,  or  upon 
a  plate  of  colored 
glass  (see  No. 
XXIV),  and  then 
pass  by  reflection 
to  a  white  wall. 
Compare   the   color  ^*'*  ^■-• 

of  this  reflected  light  with  that  reflected  at  the  same  time 
and  in  the  same  way  by  an  ordinary  mirror  (No.  22). 


The  reflecting  surface  which  we  make  use  of  in  a  common 
mirror  is  not  the  front  surface  of  the  glass,  but  the 
metallic  surface  at  the  back.  The  glass  is  merely  a  con- 
venient transparent  support  for  the  metallic  layer,  keep- 
ing it  in  shape  and  protecting  it  from  being  tarnished,  as  it 
soon  would  be  if  exposed  to  the  air. 

When  we  place  an  object  in  front  of  such  a  mirror  and 
stand  in  a  proper  position  we  see  an  image,  or  "  reflection," 
of  the  object,  and  we   say  that  we  see  the  object,  or  its 

image,  in  the  mirror.  If  M, 
Fig.  53,  is  the  mirror,  0  a 
point  of  the  object,  and  P^,  P, , 
P,,  and  P^  are  the  positions 
of  four  eyes,  all  may  see  at 
the  same  time  an  image  of  the 
point  0  in  the  mirror.  Our 
first  exercise  in  light  is  intended 
to  answer  the  question  whether  all  these  eyes  see  the  same 
image,  that  is,  whether  all  are  looking  toward  the  same 


■M 


•^ 


•O 


Fig.  53. 


'P. 


72 


PHYSICAL  EXPERIMENTS. 


point,  and  if  so,  where  this  point  is- 
or  behind  it,  or  at  its  surface. 


-in  front  of  the  mirror, 


EXERCISE  19. 

IMAGES  IN  A  PLANE  MIRROR. 

Apparatus :  A  mirror  (No.  22).  A  rectangular  block  (No.  9). 
Two  rubber  bands  to  hold  the  mirror  to  the  block.  T'wo  straight- 
edged  wooden  rulers  (Nos.  23a  and  23b).  A  measuring- stick 
(No.  3).  A  sheet  of  thin  w^hite  paper  about  12  inches  by  20 
inches.  A  small  block  (No.  24).  Attach  the  mirror  to  the  Izirge 
block  by  means  of  rubber  bands  in  the  manner  shown  by  Fig.  54, 


Fig.  54. 

taking  care  that  there  shall  be  no  twist  in  that  part  of  each  band 
which  lies  beneath  the  block,  for  such  a  twist  causes  the  block  to 
rest  unsteadily  and  be  easily  moved  out  of  place. 

Draw  a  straight  pencil-mark  across  the  sheet  of  paper  at  its 
middle,  and  set  the  back  surface  of  the  mirror  directly  over  and 
parallel  to  this  line,  the  middle  of  the  mirror  being  very  near  the 
centre  of  the  sheet.     See  Fig.  55. 

Draw^  on  the  sheet  of  paper  in  front  of  the  mirror  a  triangle, 
each  side  of  Tvhich  should  be  several  inches  long,  and  no  corner 
of  which  should  be  less  than  three  inches  from  the  mirror.  It  is 
w^ell  to  have  one  angle  of  the  triangle  not  directly  in  front  of  the 
mirror,  but  somewhat  to  one  sido,  like  point  No.  1  in  the  figure. 

Place  the    small  block   in  such  a  position   that  the  vertic2il 


LIGHT. 


73 


pencil-mark  which  it  bears  shall  be  directly  over  point  No.  1  of 
the  triangle.  Now  lay  a  straight-edged  rioler 
upon  the  paper  in  such  a  position  that  one  of 
its  long  horizontal  edges  shall  point  directly 
toward  the  image  of  the  vertical  pencil-mark, 
as  seen  in  the  mirror.  (Many  persons  cannot 
do  this  at  first  unless  they  are  especially  in- 
structed. Let  the  line  along  which  the  pupil 
is  to  sight  be  PQ  (Fig.  56),  P  being  the  point 
nearer  the  eye.  A  person  vrho  is  not  near- 
sighted should  hold  his  eye  eight  or  ten  inches 
distant  from  P,  and  should  then  direct  the  ruler 
in  such  a  way  that  the  point  P,  the  point  Q,  and 
the  image  of  the  vertical  pencil-mark  seen  in 
the  mirror,  may  all  lie  in  one  straight  line.  Do 
not  try  to  look  along  the  vertical  side  of  the 
ruler,  but  hold  the  eye  high  enough  to  see  all 
the  time  the  top  of  the  ruler,)  Then  with  a  well- 
sharpened  pencil  draw  upon  the  paper  a  fine  clear  mark  alongside 
that  edge  of  the  ruler  which  lies  just  beneath  the  line  PQ{Fig.  56) 
along  which  the  sight  has  been  taken.    Mark  this  line  1,  because  it 


r                    0 

v 

Fig.  55. 


Fig.  56. 


points  toward  the  image  of  the  vertical  pencil-mark  when  this 
msirk  is  over  point  No.  1.  Next,  without  disturbing  anything  else, 
place  the  ruler  in  a  new  position,  well  removed  firom  the  position 
just  occupied,  sight  as  before,  draw  another  line  alongside  the 
ruler,  and  mark  this  line  also  1 .  Then  with  the  ruler  in  a  new 
position,  about  half-way  between  the  first  two,  if  this  is  con- 
venient, draw  a  third  line  in  the  same  way  and  mark  this  also  1. 
All  this  time  the  small  block  has  remained  unmoved  and  the 
pencil-mark  upon  it  has  pointed  straight  dow^n  at  point  No.  1. 
liow  place  the  small  block  so  that  the  pencil-mark  will  point 


74  PHYSICAL  EXPERIMENTS. 

straight  down  at  point  No.  2.  While  it  is  in  this  position  draw 
three  straight  lines  toward  the  image  and  mark  each  one  of  these 
2. 

Finally,  put  the  pencil-mark  over  point  No.  3,  draw  three 
straight  lines  toward  its  image,  and  mark  each  of  them  3. 

(While  drawing  all  these  lines  the  pupil  should  look  frequently 
to  see  w^hether  the  back  of  the  mirror  remains  in  place.  It  may 
be  throw^n  out  of  place  by  a  little  blow  or  by  rubbing  the  paper 
hard  to  remove  pencil-marks.) 

When  the  three  sets  of  lines  have  been  drawn,  the  two  blocks 
and  the  mirror  are  removed  from  the  paper,  and  each  line  is  then 
lengthened  until  it  crosses  both  the  others  of  the  same  set ;  that  is, 
each  No.  1  line  is  continued  toward  or  beyond  the  mirror  till  it 
crosses  the  two  other  No.  1  lines.  Then  the  No.  2  set  and  the  No. 
3  set  are  treated  in  the  same  way.  (If  a  line  has  to  be  extended 
far  it  is  well  to  use  two  rulers,  A  and  B,  as  shown  in  Fig.  57.  First 


IT 


:r. 


Fig.  57. 

A  is  put  into  position  and  a  line  is  drawn  alongside  it.  Then, 
while  A  remains  unmoved,  B  is  carefully  brought  close  to  it,  as 
the  figure  show^s ;  then  B  is  held  firmly  in  place  while  A  is  pushed 
forward  to  the  position  indicated  by  the  dotted  lines.  B  is  then 
removed  without  disturbing  A,  and  again  a  line  is  drawn  alongside 
A.  In  this  way  a  line  may  be  continued  nearly  straight  for  a  con- 
siderable distance.) 

After  each  set  of  lines  has  been  extended  in  this  way,  it  'will  be 
in  order  to  answer  the  question  w^hether  all  the  lines  of  any  one 
set  lead  to  the  same  point  or  neeirly  so,  and,  if  so,  vrhere  is  this 
point  situated  with  respect  to  the  mirror  and  to  the  point  whose 
image  it  is. 

If  the  image' of  each  point,  No.  1,  No.  2,  and  No.  3,  can  be  thus 
found,  connect  the  imdige-poinis  with  each  other  by  straight  lines 
and  thus  make  an  ivadige-tr (angle. 

Then  fold  the  sheet  of  paper  carefully  along  the  pencil-mark  by 
which  the  mirror  was  placed,  and  holding  the  folded  sheet  against 


LIGHT. 


75 


a  window,  so  that  the  light  from  without  will  shine  through  it, 
compare  the  size  and  shape  of  the  two  triangles  and  their  relative 
positions  with  respect  to  the  line  along  which  the  paper  is  folded. 
The  general  rule  for  placing  the  image  of  any  point  should  be 
recorded  when  it  is  found. 


The  final  result  aimed  at  in 
this  exercise  should  be  to  enable 
the  pupil  to  tell,  wthout  further 
experiment,  in  any  new  case 
given  him,  Fig.  58,  for  instance, 
in  w^hich  J.^  is  the  line  upon 
w^hich  a  mirror  stands,  the  posi- 
tion of  the  image  of  points  No. 
1,  No.  2,  No.  3,  and  No.  4,  and 
so  the  shape  and  position  of 
the  image  of  the  figure  at  the 
corners  of  which  these  points 
Ue. 


-B 


Fio.58. 


Suggestions  for  the  Lecture-room. 

On  the  basis  of  the  pupils'  work  in  the  laboratory,  which 
has  shown  where  to  locate  the  image  /  of  a  point  0  placed 

in  front  of  a  mirror  MM, 
Fig.  59,  prove  that  the  "  an- 
gle of  incidence"  i,  which 
a  ray  from  0  striking  the 
mirror  at  C  makes  with  the 
line  CD  drawn  at  right 
angles  with  the  mirror  sur- 
face, is  equal  to  the  "  an- 
gle of  rep^ection,"  r,  made 
by  the  same  ray  with  the 
same  line  CD  after  reflec- 
tion. 

The  line  of  proof  is  as 
follows:   Atigles   at  E  are 
riglit  angles;  EI  =.  E0\  EC  is  common  to  two  triangles; 


76  PHYSICAL  JSXPERIMENTS. 

hence  triangle  CEI  is  similar  to  triangle    CEO.     Tlien 
angle  i  =  angle  EOC  =  angle  EIG  =  angle  r. 

We  have  not  yet  defined  an  image  in  strict  terms.     We 
now  see  that  the  image  I  (Fig.  60)  of  a  point  0,  placed  he- 


FiG.  60. 

fore  a  plane  mirror.  A,  is  the  point  from  ichicli  the  rays  of 
light  that  go  from  0  to  the  mirror  appear  to  diverge  after 
reflection. 

As  the  rays  really  do  not  come  from  /after  reflection, 
but  only  appear  to  do  so,  this  kind  of  image  is  said  to  be 
unreal,  or  apparent.  It  is  often  called  a  virtual  image. 
We  shall  by  and  by  find  images  that  are  real,  images  that 
will  show  on  a  white  paper  or  cloth  placed  in  the  right 
position. 

If  any  of  the  rays  from  0  (Fig.  61)  after  reflection  from 
the  mirror  A  fall  upon  a  second  plane  mirror  B,  they  will 
be  treated  by  this  second  mirror  just  as  if  they  really  came 
from  7, ;  that  is,  we  shall,  looking  into  the  mirror  B  in  the 
right  direction,  see  an  image  of  the  image  /, ,  and  this 
second  image,  7, ,  will  appear  just  as  if  it  were  the  image 
of  an  actual  object,  sending  rays  from  7,  „ 


LIGHT. 


77 


The  rays  reflected  first  from  A  and  next  from  B  might 

then  fall  upon  a  third  mirror,  and  give  an  image  of  the 

^^n'lx     image  I^,  and  so  on;   but 

at  each  reflection  there  is 

some  loss  of  light,  and  an 

.^  image  formed  after  many 

reflections  might  be  dim. 

Let  us  consider  the  im- 
ages of  a  point  0  formed 


Fig.  61. 


by  two  plane  mirrors  A  and  B  (Fig.  62),  making  with  each 
other  an  angle  slightly  less  than  90°.  We  shall  have  one 
image,  /„  formed  by  mirror  A  without  any  help  from  mirror 
B.  We  shall  have  another  image,  Z, ,  formed  by  mirror  B 
without  any  help  from  mirror  A.  There  is  also  /, ,  the 
image  of  7,  seen  in  B,  and  I^,  the  image  of  /,  seen  in  A, 
We  cannot  with  this  arrangement  of  the  mirrors  get  images 
of  I^  and  /^ ,  for  rays  leaving  mirror  A  as  if  diverging  from 
I^  would  not  strike  either  mirror  again,  and  rays  leaving 
mirror  B  as  if  diverging  from  /,  would  not  strike  either 
mirror  again. 

If  the  angle  between  the  mirrors  is  made  sufficiently 
acute,  however,  the  number  of  images  to  be  seen  may  be 
greatly  increased.  All  the  images  appear  to  be  as  far  from 
the  corner  Cas  the  original  point  0  is;  that  is,  the  point 
0  and  all  its  images  are  ranged  on  the  circumference  of  a 
circle  whose  centre  is  at  C. 


78 


PHYSICAL  EXPERIMENTS. 


EXERCISE   20. 

COMBINATION  OF  TWO  PLANE  MIRRORS :  KALEIDOSCOPE. 

Apparatus:  Two  mirrors  (No.  22).  Two  blocks  (No.  9).  A 
straight-edged  niler  (No.  23).  A  paper  protractor  (No.  25).  Four 
rubber  bands.    A  sheet  of  white  paper. 

To  study  further  the  e£fect  of  combining  two  mirrors,  and  to  see 


x 

Fio.  63. 

how^  the   number  of  images  formed  in  any  given  case  depends 
upon  the  angle  between  the  two  mirrors,  proceed  as  follow^s :  Lay 


\ 


Fio.  64. 


Fro.  65. 


off  on  the  sheet  of  paper  an  angle  of  90°,  and  about  one  inch  from 
the  apex  of  the  angle  draw  upon  the  paper  a  short,  wide  arrow 


LIGBT.  79 

(Fig.  63).  Then  place  the  two  mirrors  so  that  their  reflecting  s\u-- 
faces  will  be  just  over  and  parallel  to  the  two  lines  inclosing  the 
angle,  supporting  the  mirrors  as  in  Fig.  63. 

Looking  into  the  mirrors,  count  the  w^hole  number  of  images  of 
the  arrow  visible  in  both  of  them,  and  then  draw  a  diagram  repre- 
senting the  arrow^  and  its  images  in  their  proper  positions  vrith 
respect  to  each  other,  beginning  in  this  way — Fig.  64. 

Do  the  same  thing  with  an  angle  of  60°,  if  time  permits,  begin- 
ning the  final  diagram  as  in  Fig.  65. 

(Tw^o  pupils  w^ill  have  to  w^ork  together  in  this  exercise  unless 
two  mirrors  can  be  supplied  to  each  pupil.) 

Suggestions  for  the  Lecture-room. 

Velocity  of  light  as  found  by  observations  on  Jupiter's 
satellites  and  by  Fizeau's  method.  (Consult  almost  any 
college  text-book  of  general  physics.) 

Exhibit  the  camera  obscura  (No.  XXV)  described  in  the 
Appendix,  and  show  how  it  is  made. 

Exhibit  apparatus  for  the  next  Exercise,  and  define  co7i- 
vex,  cylindrical,  and  centre  of  curvature  (centre  of  circle, 
see  below). 

EXERCISE    21. 

IMAGES  FORMED  BY  A  CONVEX  CYLINDRICAL  MIRROR. 

Apparatus  :  The  mirror  and  its  support  (No.  26).  A  measuring- 
stick  (No.  3).  Small  block  (No.  24).  Rulers  (No.  23  a  and  b). 
Sheet  of  white  paper.  Also  the  plane  mirror  (No.  22)  and  its  sup- 
porting block  (No.  9). 

Hold  the  board  carrying  the  mirror  horizontal,  and  look  at  the 
image  of  your  own  face  in  the  convex  surface  of  the  mirror.  You 
will  see  that  the  image  is  distorted,  appearing  too  narrow  for  its 
length.  Hold  the  board  vertical  and  the  image  will  be  distorted 
in  the  opposite  w^ay,  appearing  too  wide  for  its  length.  The  ob- 
ject of  the  following  experiments  is  to  give  you  a  better  under- 
standing of  these  curious  effects. 

Set  the  mirror-base  on  the  table  and  bring  one  end  of  the 
plane  mirror  close  to  the  surface  of  the  curved  mirror,  as  in 
Fig.  66.     Then  place  the  small  block   in  front  of  both  mirrors, 


80 


PHYSICAL  EXPERIMENTS. 


as  in  Fig.  56,  in  such  a  position  that  yon  can  see  the  block  re> 

fleeted  in  both  mir- 
rors at  the  same  time. 
Do  the  tvro  im- 
ages thus  seen  appear 
of  the  same  height  ? 
Do  they  appear  of 
the  same  -viridth  ? 
Fill  out,  if  you  can, 
the  following  state- 
ment: Lines  of  the 
object  which  are  par- 
allel to  the  straight 
lines  of  the  cylindrical 

mirror  appear 

in 

the  cylindrical  mirror 


J 
Fig.  66. 


plane  mirror. 

Lines  of  the  object  which  are  at  right  angles  with  the  straight  lines 

of  the  cylindrical  mirror  appear in  the  cylindrical 

mirror in  the  plane  mirror. 

Place  the  mirror-base  On  the  sheet  of  paper  and  draw  around 
it  a  pencil-mark,  marking  the  point 
C,  Fig.  67,  as  the  centre  of  cur- 
vature. About  5  cm.  from  the  front 
of  the  mirror  draw  an  arrow  6  cm. 
long,  marking  the  ends  and  the  mid- 
dle as  in  Fig.  67.  Then  place  the 
small  block  so  that  the  vertical  pen- 
cil-mark which  it  carries  will  point 
straight  down  at  point  No.  1. 

With  the  straight-edged  ruler  draw 
two  lines,  well  apart,  toward  the 
image  of  this  vertical  line  as  seen 
in  the  mirror,  avoiding  parts  of  the 
mirror,  if  there  are  such,  that  do  not 
give  a  good  image  of  the  line.  Meirk  each  of  these  lines  1. 
Then  draw  two  lines  for  point  No.  2  and  two  for  point  No.  3, 
in  the  same  w^ay. 

Then  clear  the  paper  and  prolong  each  pair  of  lines  till  it  comes 
to  a  crossing-point.    The  three  points  thus  foiuid  will  locate  the 


i-«^- 


■>5 


Fio.  67 


LIQBT. 


81 


images  of  object-points  No.  1,  No.  2,  and  No.  3,  respectively,  and 
a  line  connecting  these  three  image-points  will  give  an  idea  of  the 
shape  of  the  image-eurrovr,  whether  it  is  straight  or  not,  and 
whether  its  curvature,  if  it  has  any,  is  in  the  same  gei^eral  direc- 
tion as  the  curvature  of  the  mirror  or  in  the  opposite  direction. 

Draw  a  straight  line  from  each  marked  olg'ect-point  to  the  cor- 
responding image-point,  and  prolong  these  three  lines  until  they 
cross  each  other.    Note  where  the  crossing  occurs. 


Is  the  image  longer  or  shorter  than  the  object  ?  Is  it  nearer  to, 
or  farther  from,  the  mirror  tham  the  object  is  ? 

(It  must  be  understood  that  the  pupil  is  asked  these  questic  ns 
only  in  regard  to  the  particular  case  that  he  has  tried.  He  cannot 
tell  without  further  experiments  or  further  instruction  whether 
the  answers  he  gives  in  this  case  would  be  true  for  all  cases  of 
objects  reflected  in  mirrors  such  as  he  is  using,  for  he  does  not 
know  that  the  distance  of  the  object  from  the  mirror  may  not  de- 
cide all  these  questions.  The  fact  is,  however,  that  if  he  has 
found  correct  answers  to  the  questions  asked  for  his  one  case, 
the  same  answers  will  be  true  for  the  same  questions  in  all  cases 
with  convex  cylindrical  mirrors.  The  efifects  seen  with  coneate 
mirrors  are  much  more  complicated.) 

Suggestions  for  the  Lecture-room. 

"With  curved  mirrors,  as  with  plane  mirrors,  the  law 
angle  of  incidence  =  angle  of  reflection  holds.  With  the 
help  of  this  law  we  can  see 
why  the  image  of  a  point  is 
nearer  the  mirror,  when  this 
is  convex,  than  the  point 
itself  is. 

Let  0,  Fig.  68,  be  the 
object-point  in  front  of  the 
convex  mirror  MM,  the 
centre  of  curvature  being  at 
C.  A  line  drawn  from  C  to 
any  point  of  the  mirror  is  at 
right  angles  with  the   mirror  at  the   point  of  crossing. 


^ 


PHT8IGAL  BXPERTMENT8. 


Two  rays  going  from  0  to  the  mirror-front  appear  after 
reflection  to  come  from  /,  which  is  nearer  the  mirror  than 
Ois. 

If  the  concave  side  of  the  mirror  were  used,  it  is  easy  to 
see  from  Fig.  69  that  rays  from  a  point  0  near  the  mirror- 


a' 


front  would  after  reflection  ap- 
pear to  come  from  a  point  /, 
which  is  farther  from  the  mir- 
ror than  0  is. 
It  is  evident  that  the    rays 


from  0  are  more  nearly  parallel  to  each  other  after  reflection 
than  before.  Rays  from  a  point  0',  somewhat  farther  from 
the  mirror  than  0,  appear  after  reflection  to  come  from  a 
still  more  distant  point,  /',  and  these  rays  are  nearly  parallel 
after  reflection.  It  is  easy  to  see  that  if  the  object-point 
were  put  somewhat  farther  still  from  the  mirror,  the  rays 
proceeding  from  it  might,  after  reflection,  be  parallel  to 
each  other.  They  would  appear  to  come  from  a  point  as  far 
as  possible  behind  the  mirror. 

If  the  object-point  is  placed  still  farther  away  from  the 
mirror,  as  at  0  in  Fig.  70,  the  rays  will  after  reflection  be 
actually  converging,  and  will  cross  at  a  point  /in  front  of 


LIGHT. 


83 


the  mirror.  This  image  /  is  a  real  image  (see  remarks 
following  Exercise  19),  and  if  0  is  bright  enough,  the  image 
/may  be  seen,  like  a  picture,  on  a  piece  of  white  paper 
or  cloth  placed  in  the  right  position. 

If  the  object-point  were  placed  where  /  now  is,  the  image- 
point  would  fall  where  0  now  is.  We  see  that  the  centre 
of  curvature  C  lies  between  the  object-point  0  and  the 
image-point  I  in  these  two  cases.  This  is  always  so  in  the 
case  of  real  images  formed  by  concave  mirrors,  unless  the 
object-point  is  at  C,  in  which  case  the  image-point  also 
falls  at  Q. 

EXERCISE  22. 

CONCAVE    CYLINDRICAL    MIRROR. 

Apparatus:  The  same  as  in  the  preceding  Exercise,  and  in 
addition   a  common   pin   and   two 
wooden  toothpicks    (or    any    tw^o 
straight,  slender     o1:jects    3   or   4 
inches  long). 

From  two  points  about  4  cm. 
apart  on  the  mirror-front  draw^  two 
radii,  r  r,  on  the  base-board  sup- 
porting the  mirror,  as  in  Fig.  71, 
extending  them  to  the  centre  of 
curvature  C.  Draw  arrow  A  about 
0.8  cm.  distant  from  the  mirror-front 
and  B  about  1.5  cm.  distant.  Draw 
D  about  1.5  cm.  distant  from  the 
centre  of  curvature  C.  (All  of  this 
work  should  be  done  for  the  pupils 
before  the  class-work  begins.) 


Fig.  71. 


Let  the  pupil,  holding  the  mirror  about  10  inches  from  his  eye, 
look  at  the  images  oi  A,  B,  and  D. 

Do  the  images  of  A  and  B  point  in  the  same  general  direction, 
from  left  to  right  in  the  figure,  as  the  arrows  themselves  ? 

Is  the  same  answer  true  of  D  and  its  image  ? 

Are  the  images  of  A  and  B  longer  or  shorter  than  the  arrQws 
themselves  ? 


84  PHYSICAL  EXPERIMENTS, 

At  the  centre  of  A  stand  the  pin  upright,  and,  laying  the  two 
toothpicks  on  the  base-board,  point  them  toward  the  image  of  the 
pin,  contriving  to  have  them  make  a  considerable  angle  with  each 
other.  In  this  way  the  position  of  the  image  is  located.  Is  it  be- 
hind the  mirror  or  in  front  ? 

Is  it,  then,  a  real  image  or  an  unreal  one  ? 

By  the  same  method  locate  the  image  of  the  pin  when  erected 
at  the  centre  of  B  and  when  at  the  centre  of  D,  asking  and  an- 
swering in  each  case  the  same  questions  that  were  asked  when  the 
pin  was  at  the  centre  of  A. 

If  time  permits,  continue  the  Exercise  as  follows : 
Place  the  mirror  on  a  sheet  of  paper  and  extend  the  two  radii, 
r  r  by  the  lines  r'  /  drawn  on  the  paper,  as  in  Fig.  71.  Draw  the 
arrow  E,  6  or  8  cm<  distant  from  C,  marking  points  1,  2,  and  3 
upon  it.  Ijocate  the  image  of  each  of  these  points  by  the  method 
used  in  the  preceding  Exercise  with  the  convex  side  of  the 
mirror,  drawing  upon  the  paper  the  lines  of  sight  and  the  image  of 
the  arrow. 

Suggestions  for  the  Lecture-room. 
Curved  mirrors  made  for  common  use  are  usually  parts 
of  spherical  surfaces.      The  effects    produced    by  such 
mirrors  are  really  simpler  than   those 
^  produced  by  cylindrical  mirrors. 

With  a  concave  spherical  mirror  5  or 

6  inches  wide  (No.  XXVI)  interesting 

lecture-table  experiments  may  be  made 

^Q         ■  in  a  slightly  darkened  room,  the  image 

^  of  a  candle-flame  or,  better,  gas-flame 

^*  being  thrown  upon  a  screen  so  as  to 

be  visible  to  all  in  the  room.     The 

screen  should   be  of  tracing-cloth  or 

oiled  paper,  so  that  the  image  upon  it 

may   be  seen  from    both    sides.      An 

opaque  screen  should   hide  the  flame 

^ itself    from    the    eyes  of  the    pupils. 

®'  Fig.  73  suggests  a  good  arrangement, 

MM  being  the  mirror,  C  its  centre  of  curvature,  L  the 


LIGHT.  85 

flame,   8  the    opaque    screen,  and  S'  the    tracing-cloth 
screen. 

The  positions  of  L  and  S  may  be  greatly  varied  and 
may  be  interchanged,  but  the  least  distance  of  either  from 
the  mirror  should  be  rather  more  than  one  half  the  radius 
of  curvature  of  the  mirror,  if  real  images  are  desired. 


86  PHYSICAL  EXPERIMENTS. 


CHAPTER  VIII. 

REFRACTION. 

In  the  experiment  made  with  a  prism  the  class  may  have 
noticed  that  the  light  did  not  go  in  the  same  direction 
after  leaving  the  prism  as  before  entering  it.  Some  mem- 
bers of  the  class  in  looking  into  pools  or  vessels  of  water 
may  have  noticed  that  objects  beneath  the  surface  are  not 
exactly  where  they  seem  to  be. 

EXPERJMENT. 

Place  a  straight  stick  in  an  oblique  position,  partly  in 
and  partly  out  of  water.  Exhibit  this  to  the  class  in  sev- 
eral aspects,  showing  the  apparent  bending  or  disconnec- 
tion of  the  stick  at  the  surface  of  the  water. 

These  curious  effects  are  due  to  the  fact  that  when  light 
goes  obliquely  from  air  into  water  or  glass,  or  any  other 
transparent  body,  or  when  it  comes  out  obliquely  from  any 
such  body  into  air,  it  suffers  a  change  of  direction  just  at 
the  surface  of  the  body.  This  change  of  direction  is  called 
refraction. 

The  amount  of  the  bending,  or  refraction,  which  a  ray 
of  light  suffers  at  any  surface  depends  partly  upon  the 
two  substances  which  meet  at  this  surface,  and  partly 
upon  the  angle,  i,  Fig.  73,  which  the  ray  makes  with  a 
line  NN,  which  is  at  right  angles  with  the  surface  at 
the  point  C  where  the  ray  strikes  the  surface. 

If  the  space  above  the  line  AB  represents  the  air- 
space, and  that  below  this  line  the  water,  or  glass,  or 


REFRACTION. 


87 


whatever  substance  it  may  be  that  lies  there,  solid  or 
liquid,  the  course  of  the  ray  is  changed  at  the  surface  in 
such  a  way  that  the  angle  r  which  it  makes  with  NN 
inside  the  solid  or  liquid  is  smaller  than  the  angle  i. 

The  angle  i  in  Fig.  73  is 
called  the  aiigle  of  inci- 
dence. The  angle  r  is  called 
the  angle  of  refraction. 

If  the  ray  were  represented 
as  coming  in  the  opposite 
direction,  that  is,  first  along 
R  and  then  along  I,  r  would 
be  the  angle  of  incidence 
and  i  would  be  the  angle  of 
refraction.  The  ray  would 
be  bent  just  as  much  at  the 
surface  as  it  is  when  going  first  along  /  and  then  along  R. 

When  the  direction  of  /is  changed  the  direction  of  R  is 
changed.  The  way  in  which  the  change  of  one  depends 
upon  the  change  of  the  other  is  easily  shown  by  means  of 
Fig.  74.  /,  /',  and  /"  show  three  rays  all  of  which  come 
to  the  point  C  and  then  separate,  the  first  going  along  R, 
the  second  along  R' ,  the  third  along  R" .  The  circle 
whose  centre  is  at  C  is  drawn  with  any  convenient  length 
of  radius.  The  dotted  lines,  n,  n',  n",  and  m,  m',  m",  are 
drawn  from  the  points  where  the  rays  cut  the  circum- 
ference to  the  line  NN  at  right  angles. 

If  this  figure  has  been  drawn  so  as  to  accord  with  the 
results  of  experiments  on  light  rays,  we  shall  have 


71 

m 


n' 

a? 


m 


and  any  one  of  these  equal  ratios  is  called  the  index  of 
refraction  from  the  substance  or  medium  through  which  the 
ray  comes,  to  the  substance  or  medium  into  which  it  goes, 


88 


PHYSICAL  EXPERIMENTS, 


If  now  we  can  measure   —  in  any  given  case,  we  shall 

have  a  quantity  which  is  very  useful  in  physics,  for  by 
means  of  it  we  can  calculate  at  once  the  value  of  a  new  m 


to  go  with  any  new  w;  that  is,  we  can,  if  we  know  the 
angle  which  any  ray  makes  with  XJV^in  one  medium,  find 
without  further  experiment  the  angle  which  the  same  ray 
makes  with  NN  in  the   second   medium.     Exercise   23 

Oh 

shows  how  to  find  the  ratio  —  for  the  case  of  air  and  water. 

m 


EXERCISE    23. 
INDEX  OF  REFRACTION  FROM  AIR    TO    WATER. 

Apparatus :  Articles  Nos.  3, 14,  15,  23a,  23b,  27,  28,  and  a  sheet 
of  paper  about  6  inches  square. 

Put  the  partition  N  in  place,  as  shown  in  Fig.  75,  and  pour 
water  into  the  jar  until  its  surface  comes  within  1  or  2  mm,  of  the 
middle  tooth  of  the  partition.  Then  by  means  of  the  plunger  (No. 
14),  attached  to  the  side  of  the  jar  by  means  of  its  clasp,  raise  the 
level  of  the  water  till  the  apparent  distance  between  the  middle 


REFRACTION. 


89 


tooth  of  the  partition  and  its  reflection  in  the  water  surface  is  less 
than  1  nun.  (To  see  this  reflection  well,  one  should  look  through 
the  wall  of  the  empty  part  of  the  jar. 

Then  the  brass  index  h  is  attached  to  the  jar,  as  shoira  in  Fig. 
75,  and  is  raised  or  lowered  until  an  eye  on  the  line  Cg,  8  or  10 
inches  from  the  jar,  can  barely  see  p,  the  very  tip  of  b,  apparently 
in  a  straight  line  with  Cg.  This  setting  should  be  made  with  care, 
and  after  it  is  made  the  experimenter  must  look  to  see  whether 
the  tooth  at  C  is  clear  of  the  w^ater.  If  its  lowest  edge  touches  the 
w^ater  the  setting  is  useless,  and  all  of  the  adjustments  most  be 
made  anew  before  a  reading  is  made. 


P 


d/-Vl. 


Fig   76. 


Fig.  75. 


When  all  the  adjustments  have  been  successfully  made,  measure 
carefully  the  distance  from  the  top  of  the  jar  down  to  the  tip  p  of 
the  index,  the  measuring-stick  being  kept  outside  the  jar.  (The 
tip  p  should  be  close  against  the  glass). 

Measure  now  the  inside  diameter  of  the  jar. 

Measure  also,  unless  it  is  already  known,  the  distance  of  C  below 
the  top  of  the  jar.  (It  is  well  to  have  this  distance,  which  is 
somew^hat  troublesome  to  measure  accurately,  given  by  the 
teacher.  Partitions  of  different  depth  might  be  used  in  order  to 
vary  the  angles  of  incidence  and  refraction.) 

Now  make  a  drawing,  of  full  natural  size,  of  the  sides  of  the  jar, 
the  water  surface  and  the  partition,  as  in  Fig.  76,  continuing  the 
partition  line,  by  means  of  dots,  well  down  into  the  jar.  Put^  in 
its  proper  place,  and  then  draw^  the  lines  pC  and  Cg. 

Now^  w^ith  C  as  a  centre  and  with  any  convenient  radius,  Cg  for 
instance,  one  may  draw  a  circle  cutting  CP  at  d.     Then,  since  pC  is 


90 


PHYSICAL  EXPERIMENTS. 


the  course  of  a  ray  of  light  in  the  water,  and  Cg  the  course  of  the  same 
ray  after  leaving  the  water,  the  index  of  refraction  from  water  to 

air  is  — ,  while  the  index  of  refraction  from  air  to  water  is  — .      (It 
n  m 

is  customary  to  state  the  index  of  refraction /rom  air  to  water.)    It 

is  evident  that  the  circle  need  not  be  drawn.    It  is  just  as  well  to 

find  the  point  d  by  measuring  oflf  Cd  equal  to  Cg. 

If  the  jar  used  in  this  Exercise  is  not  pretty  level  at  the  top, 
or  if  the  partition  is  not  just  at  the  middle  of  the  jar,  it  is  well, 
after  making  one  setting  of  the  index  and  one  measurement  of  its 
position,  to  turn  the  jar  about,  transferring  the  index  to  the  other 
side,  and  make  a  newr  setting  and  a  new  measurement.  The  mean 
of  the  two  measurements  thus  made  should  be  nearly  free  from 
any  error  caused  by  irregularity  of  the  jar  or  of  the  partition's 
position.) 

Suggestions  for  the  Lecture-room. 

If  light  goes  through  a  transparent  plate  whose  sides  are 
parallel  to  each  other,  the  refraction  at  the  second  surface 
undoes  that  which  happens  at  the  first  surface,  and  the 

light  has  the  same  direc- 
tion after  leaving  the  plate 
as  before  entering  it.  See 
Fig.  TT.  Light  passing 
through  a  prism  (see  Fig. 
78),  usually  suffers  at  the 
second  surface  a  further 
^^^-  '^-  bending    away    from     its 

original  direction.    The  separation  of  colors  by  which  the 


Fig.  78. 


REFRACTION. 


91 


prism  produces  what  is  called  a  spectrum  is  due  to  the  fact 
that  the  different  kinds   of  light   are 
bent   different  amounts  by  the  prism. 
Blue  or  violet  is  refracted  most  and 
red  least. 


When  we  look  straight  down  into 
water  at  any  small  object  it  appears 
to  be  in  its  true  direction  from  the 
eye,  but  nearer  than  it  really  is.  Fig. 
79  indicates  why  this  is  so.  0  represents  the  object,  E 
the  eye,  and  0'  the  apparent  position  of  the  object. 


Lenses. 

A  lens  is,  usually,  a  piece  of  glass  whose  two  faces  are 
parts  of  spherical  surfaces. 

Sometimes  there  is  a  cylindrical  surface  between  the  two 
spherical  faces. 

Fig.  80  shows  various  lenses  as  they  Avould  look  if  cut 
through  the  middle. 


Fig.  80, 

The  lenses  we  shall  use  will  be  much  like  No.  1  in  this 
figure.     The  two  sides  are  supposed  to  be  just  alike. 

To  understand  such  a  lens  better  we  will  make  use  of 
Fig.  81. 

C,  is  the  centre  of  the  spherical  surface  of  which  ASB 


92 


PHYSICAL  EXPERIMENTS. 


is  a  part.     It  is  called  the  centre  of  curvature  of  the  face 
ASB.     C.  is  the  centre  of  curvature  of  the  face  ARB. 


Fig.  81. 

The  straight  line  CfiG^,  continued  to  any  distance  in 
each  direction,  is  called  the  principal  axis  of  the  lens. 

Any  straight  line  going,  like  LM,  obliquely  through  the 
centre  of  the  lens  is  called  a  secondary  axis  of  tlie  lens. 

If  the  two  faces  of  a  lens  are  exactly  alike,  as  we  suppose 
them  to  be  here,  any  ray  of  light  going  through  the  centre 
of  the  lens,  the  point  0,  will  have  the  same  direction  after 
leaving  the  lens  as  before  entering  it,  because  the  two  little 
spots  of  surface  at  which  it  enters  and  leaves  the  lens  are 
parallel  to  each  other,  so  that  the  ray  is  affected  just  as  if 
it  were  going  through  a  plate  with  parallel  faces. 

Rays  entering  a  lens.  Fig.  82,  parallel  to  its  principal 


Fig.  83. 


axis  are  refracted  in  such  a  way  that  after  leaving  the  lens 
they  will  cross  this  axis.  They  do  not  all  cross  at  one 
point,  but  if  the  faces  are  near  together,  and  are  very  small 


REPn ACTION. 


93 


parts  of  spherical  surfaces,  as  in  our  lenses,  such  rays  will 
cross  at  or  near  a  certain  point,  F,  on  the  principal  axis, 
and  this  point  is  called  i\\e  principal  focus  of  the  lens. 

The  distance  from  the  principal  focus  to  the  nearer 
face  *  of  the  lens  is  called  the  focal  length  of  the  lens. 

Focal  length  is  a  quantity  of  very  great  importance  in 
dealing  with  lenses,  and  the  next  Exercise  will  show  how 
to  find  it  by  experiment.  For  this  purpose  we  need  to 
have  the  light  come  to  the  lens  in  rays  nearly  parallel  to 
each  other  and  to  the  principal  axis.  This  we  can  do  by 
taking  the  light  from  any  small  spot  of  any  distant  but 
distinct  object ;  for  instance,  a  chimney  or  a  church  spire 
outlined  against  the  sky. 


EXERCISE  24. 

FOCAL  LENGTH  OF  A  LENS. 

Apparatus :  The  lens  mounted  on  a  block  (No.  29).  A  meter-rod 
(No.  2).  A  small  block  (No.  20)  bearing  a  white  cardboard  screen 
(No.  30).    A  common  pin. 

First  Method. 
Place  the  lens  and  the  screen  upon  the  rod,  as  in  (Fig.  83),  and 


Fig.  83. 


point  the  rod  at  some  distant  object  seen  against  the  sky  in  such 
a  -way  that  the  light  from  this  object  -will  pass  through  the  lens 

*  See  Appendix  VIII.  of  Hiill  and  Bergen's  Text-book  of  Physics. 


94  PHYSICAL  JSXPERIMENTS. 

and  then  fall  upon  the  screen.  Move  the  screen  back  and  forth 
until  that  part  of  the  image  which  lies  on  or  near  the  principal 
axis  of  the  lens  is  made  as  distinct  as  possible.  Then  by  means  of 
the  graduations  on  the  meter-rod,  or  by  an  independent  measur- 
ing-stick if  this  is  preferred,  note  the  distance  from  this  part  of 
the  image  to  the  nearer  face  of  the  lens.  This  is  the  focal  length. 
(The  image  is  formed  because  light  coming  from  any  one  small 
spot  of  the  object  is  brought  to  a  small  spot  again  by  the  lens. 
The  image  is  made  up  of  such  small  spots  each  in  its  own  place. 
For  the  purposes  of  this  class  the  distant  object  need  not  be  more 
than  30  or  40  feet  from  the  experimenter.  The  images  on  the 
screen  will  be  much  more  distinct  if  the  apparatus  is  used  in  the 
back  part  of  the  room,  well  away  from  the  windows.) 

Second  Method. 

Remove  the  screen  from  its  block  and  put  the  pin  upright  in 
its  place.  Let  the  pin,  thus  mounted,  be  placed  on  the  meter-rod, 
about  as  far  from  the  end  of  the  rod  as  the  pupil  usually  holds  a 
book  from  his  eyes  w^hen  reading.  Place  the  lens  somew^hat 
farther  from  the  same  end  of  the  rod. 

Place  the  eye  at  this  end  of  the  rod  and,  looking  sharply  at  the 
pin,  direct  the  rod  and  adjust  the  lens  in  such  a  w^ay  that  the  light 
from  some  distinct  distant  object  w^ill  pass  through  the  lens  and 
form  an  image  in  the  air  close  to  the  pin.  To  decide  whether  the 
image  is  nearer  the  eye  than  the  pin  is,  move  the  eye  to  and  fro, 
to  the  right  and  the  left,  w^atching  the  pin  and  the  image.  If  the 
pin  is  more  distant  than  the  image,  it  will,  when  the  eye  is  moved 
toward  the  right,  appear  to  move  across  the  image  toward  the 
right.  If  the  pin  is  nearer  than  the  image,  it  will,  when  the  eye  is 
moved  tow^ard  the  right,  appear  to  move  across  the  image  toward 
the  left.  The  rod  should  not  be  held  in  the  hands  during  this  test, 
but  should  be  placed  on  some  steady  support.  (To  see  the  reason 
of  this  test,  close  one  eye  and  hold  the  two  forefingers,  some 
inches  apart,  in  line  mth  the  other  eye,  so  that  one  finger  hides 
the  other.  Then  move  the  eye  to  the  right  and  left,  and  notice  the 
apparent  movement  of  the  fingers  with  respect  to  each  other.) 
Continue  the  adjustments  until  the  test  described  fails  to  show 
which  of  the  tw^o,  the  pin  or  the  image,  is  nearer  the  eye.  Then 
measure  the  distance  from  the  pin  to  the  lens.  It  should  be  the 
focal  length  of  the  lens. 


RBFR ACTION.  95 

Compare  the  values  of  the  focal  length  given  by  the  two 
methods. 

The  second  method  is  more  difficult,  but  it  gives,  perhaps,  more 
accurate  results,  and  it  can  be  used  in  cases  vrhere  the  image  is  too 
faint  to  show  clearly  upon  the  screen. 

(Each  lens  should  be  numbered  on  a  bit  of  paper  pasted  upon 
it.  Each  pupil  should  record  the  number  of  the  lens  he  uses. 
The  teacher  should  know  the  focal  length  of  each  lens.) 

Suggestions  for  the  Lecture-room. 

Were  the  images  seen  in  Exercise  24  real  or  virtual  ? 

Were  they  erect  or  inverted;  that  is,  were  they  right 
side  up  or  wrong  side  up  ? 

As  there  is  an  image  in  the  air,  the  pupil  may  not  see 
why  this  image  cannot  be  seen  by  a  whole  class  at  once 
without  the  use  of  a  screen.  It  is  because  the  light  form- 
ing the  image  in  the  air  goes  straight  on  through  this 
image,  and  can  be  received  only  by  placing  one's  self  be- 
hind the  image;  while  the  light  which  forms  an  image  upon 
a  screen  is  by  the  threads  of  the  screen  reflected  back  in  all 
directions,  and  therefore  some  part  of  it  reaches  every  eye. 

If  a  bright  point  were  placed  at  the  principal  focus  of  a 
lens,  what  direction  would  the  rays  going  from  this  point 
to  the  lens  have  after  passing  through  the  lens  ? 

In  the  next  Exercise  we  shall  ask  at  what  distance  from 
the  lens  the  image  is  when  the  object  is  not  a  distant  one. 

EXERCISE  25. 

RELATION   OF    IMAGE-DISTANCE   TO   OBJECT-DISTANCE: 
CONJUGATE  FOCI  OF   A  LENS. 

Apparatus :  The  same  lens  that  w^as  used  in  Exercise  24  (No. 
29).  A  meter-rod.  Block  (No.  9).  Small  block  (No.  20)  with  a 
cardboard  screen  (No,  30).  Small  kerosene  lamp  Turith  a  black- 
ened chimney  (No.  31), 

(To  economize  space  upon  the  laboratory-tables  it  will  probably 


96  PffT3lCAL  JSIPBRIMENTS. 

be  necessary  to  have  pnpils  work  in  pairs  in  this  Exercise. 
Each  pair  should  know  or  be  told  the  focal  length  of  its  lens  at  the 
outset,  so  as  to  lose  no  time  in  beginning  the  Exercise.) 

ArrEUige  the  apparatus  according  to  Fig.  84.     The  cross  on  the 
chimney,  lighted  up    by  the  flame  behind,  is  the  object  whose 


Fig.  84. 

image  is  to  be  received  upon  the  screen.  One  end  of  the  meter- 
rod  rests  upon  the  base  of  the  lamp,  just  beneath  the  cross. 

Place  the  screen  at  first  at  a  distance  from  the  cross  about  equal 
to  three  times  the  focal  length  of  the  lens.  Then  move  the  lens 
back  and  forth  on  the  rod  between  the  cross  and  the  screen,  and 
see  whether  in  any  position  it  gives  upon  the  screen  a  clear  image 
of  the  cross.  If  it  does,  measure  the  distance  from  the  lens  in  this 
position  to  the  cross,  and  write  this  distance  as  the  first  number  in 
a  record-column  headed  Do  (object-distance).  Measure  also  the 
distance  from  the  lens  to  the  screen,  and  put  this  distance  as  the 
first  number  in  a  record-column  headed  Di  (image-distance.) 

If,  with  the  present  position  of  the  screen  and  cross,  there  is  no 
position  of  the  lens  that  will  cause  a  distinct  image  of  the  cross  to 
fall  upon  the  screen,  move  the  screen  one  or  two  centimeters  far- 
ther from  the  cross,  and  then  try  again  to  get  a  good  image-  If 
still  none  is  found,  move  the  screen  still  farther  away,  continuing 
the  trial  till  a  distinct  image  is  obtained,  Then  measure  and  re- 
cord the  Do  and  />;  as  abready  described,  (Very  little  time  need 
be  spent  upon  these  first  successive  trials.) 

Then  at  one  move  place  the  screen  about  10  cm,  farther  still 
from  the  cross,  find  a  position  of  the  lens  that  will  give  a  distinct 
image,  measure  and  record  Do  and  D\  as  before.  Without  moving 
the  screen  see  whether  there  is  any  other  position  of  the  lens  that 
will  give  a  distinct  image.  If  there  is,  measxire  and  record  the  Do 
and  the  A  for  this  position  of  the  lens. 


REFRACTION.  97 

Move  the  screen  10  cm.  farther  away,  and  then  do  exactly  as 
before, 

If  there  is  time,  move  the  screen  two  or  three  more  times,  ad- 
justing the  lens,  measuring,  and  recording  each  time,  It  is  better 
to  make  a  moderate  number  of  settings  and  readings  well  than  a 
large  number  carelessly,  but  an  error  of  one  or  two  millimeters  in 
these  readings  will  be  of  little  consequence. 

Suggestions  for  the  Lecture-room. 

The  distance  from  object  to  image  in  any  case  of  Exer- 
cise 25  is  Do  -\-  Bi,  and  we  may  call  this  Doi.  This  dis- 
tance was  shortest  in  the  first  case  recorded.  Let  each 
member  of  the  class  divide  the  Doi  of  this  case  by  the  focal 
length  of  his  lens.  Is  the  quotient  found  by  any  one  as 
small  as  3  ?     Is  it  as  large  as  5  ? 

When  the  screen  was  farther  away,  was  there  usually 
more  than  one  position  of  the  lens  that  would  give  a  dis- 
tinct image,  the  screen  remaining  unmoved  ? 

If  you  were  told  that  in  a  given  case  the  Do  was  20  cm. 
and  the  A  60  cm.,  could  you  tell  what  the  other  possible 
Do  and  Di  would  be  for  the  same  positions  of  object  and 
screen  ?  Look  at  your  record-columns  for  Exercise  25,  and 
see  whether  they  help  you  to  answer  this  question. 

Definition. — Two  points  so  placed  with  respect  to  a  lens 
that  an  object  placed  at  either  one  of  them  will  have  an 
image  at  the  other  are  called  conjugate  foci  of  the  lens. 

Let  each  member  of  the  class  call  F  the  focal  length  of 
the  lens  which  he  used  in  Exercise  25,  and  let  him  test  the 
truth  of  the  formula 

A  =  l  +  1 

F  Do^ d: 

or,  what  means  the  same, 

DoXD,=  F{Do^D,), 


98  PHYSICAL  EXPERIMENTS. 

for  all  thp  cases  which  he  tried  and  recorded  in  Exercise 
35. 

In  the  preceding  Exercises  the  object  presented  to  the 
lens  has  been  small,  or  has  been  at  such  a  distance  as  to 
give  a  rather  small  image.  It  is  now  desii-able  to  study 
larger  images,  and  to  study  them  with  especial  reference  to 
their  shape  rather  than  their  distance  from  the  lens.  AVe 
shall  in  the  next  Exercise  find  the  shape  and  size  of  an 
image  of  an  arrow  placed  at  right  angles  with  the  princi- 
pal axis  of  the  lens  and  not  far  from  the  lens.  We  shall 
not  attempt  to  find  the  whole  image  at  once,  but  shall  find 
separately  the  images  of  several  points  of  the  arrow,  and 
then  make  an  approximate  image  of  the  arrow  by  connect- 
ing these  points. 

EXERCISE  26. 

SHAPE  AND  SIZE  OF  A  REAL  IMAGE  FORMED  BY  A  LENS. 

Apparatus:  The  lens  (No.  29).  Measuring-stick  (No.  3).  Block 
(No.  20)  carrying  in  the  narrow  slot  on  its  top  a  piece  of  wire  (No. 

32)  extending  first  horizon- 
tally and  then  downw^ard 
(see  Fig.  85).  A  ruler  (No. 
23).  Block  (No.  24).  A 
sheet  of  paper  about  1  ft, 
wide  and  3  ft.  long,  having 
near  one  end  an  arrow^  8  cm. 
long,  draw^n  at  right  angles 
vrith  a  pencil-mark  about 
30  cm.  long,  and  marked, 
or  numbered,  as  shown  by 
Fig.  85.  Weights  (No.  19) 
to  hold  the  corners  of  this 
sheet  in  place  on  the  table. 

Arrange  the  apparatus  as  shown  by  Fig.  86,  the  centre  of  the 
lens  over  a  point  on  the  long  pencil-mark,  at  a  distance  from  the 
centre  of  the  arrow  about  equal  to  li  times  the  focal  length  of  the 
lens,  block  No.  24  so  placed  that  the  vertical  mark  upon  its  face 
points  straight  down  to  point  No.  3  of  the  arrow.     This  vertical 


'^' 


Fig.  85. 


REFRACTION. 


99 


mark  will  now  cross  the  principal  axis  of  the  lens,  if  the  lens  is 
accurately  placed. 

Place  the  other  block  near  the  other 
end  of  the  paper  in  such  position  that 
the  vertical  part  of  the  wire  it  carries 
shsdl  be  near  the  principal  axis  of  the 
lens.  Keep  the  eye  8  or  10  inches  dis- 
tant from  this  part  of  the  wire,  on  a 
level  with  the  centre  of  the  lens  and  in 
line  -with  the  centre  of  the  lens  and  the 
vertical  part  of  the  wire.  Look  at  this 
part  of  the  wire  so  as  to  see  it  distinctly, 
and  note  whether  you  can  see  at  the 
same  time,  near  the  w^ire^  the  image  of 
the  pencil- mark  on  the  farther  block. 

If  so,  find  out  by  moving  the  eye  to  the  right  or  left,  as  in  Exer- 
cise 24,  whether  this  image  is  more  or  less  distant  from  the  eye 
than  the  vertical  w^ire  is.  Then  move  the  block  carrying  the  wire 
into  such  a  position  that  the  image  and  the  wire  seem  to  keep 
close  together  w^hen  the  eye  is  moved  a  considerable  distance 
to  the  right  or  left.  When  this  adjustment  is  made,  put  a  dot  on 
the  paper  just  beneath  the  vertical  wire  and  mark  this  dot  3.  It 
represents  the  image  of  olyect-point  No.  3. 

Find  in  a  similar  manner  the  image-points  1 , 2, 4,  5,  correspond- 
ing to  the  object-points  1, 2, 4,  5.  The  pupil  must  take  care  not  to 
let  any  idea  he  may  have  as  to  the  position  where  an  image-point 
ought  to  be  affect  his  judgment  in  deciding  where  it  is. 

After  jdl  the  five  image-points  are  found,  connect  them.  No.  1  to 
No.  2,  No.  2  to  No.  3,  etc.,  by  means  of  straight  lines,  thus  getting 
at  least  a  rough  representation  of  the  w^hole  image. 

Draw  from  each  object-point  tow^ard  the  corresponding  image- 
point  a  straight  line  as  long  as  the  ruler  (No.  23)  and  note  the 
point  where  these  lines  cross  each  other. 


Suggestions  for  the  Lecture-room. 

The  formation  of  the  image-points  in  Exercise  26  is 
ilhistrated  by  Fig.  87.  One  ray  from  the  object-point  A 
follows  a  secondary  axis,  passes  through  the  centre  of  the 
lens    0,  and  its  direction  after  leaving  the  lens  is  the 


100  PHYSICAL  EXPERIMENTS. 

same  as  before  entering  it.  (Its  direction  inside  the  lens 
is  not  quite  the  same,  but  the  figure  does  not  show  this.) 
Another  ray  from  xi  runs  parallel  to  the  principal  axis 


Fig.  87. 

before  entering  the  lens,  and  will  therefore  pass  through 
the  principal  focus,/,  on  the  farther  side  of  the  lens.  The 
crossing  of  these  two  rays  at  A'  shows  the  position  of  the 
image  of  A. 

In  a  similar  way  B',  the  image  of  B,  is  located. 

We  see  from  Exercise  26  and  from  Fig.  87  that,  when  an 
object-point  is  farther  from  a  lens  than  its  principal  focus 
is,  the  rays  going  from  this  object-point  to  the  lens  are 
bent  by  the  lens  in  such  a  way  that,  after  leaving  it,  they 
converge  to  a  point  again.  We  know  that  if  the  object- 
point  were  placed  at  the  principal  focus  the  rays  going 
from  it  to  the  lens  would  emerge  from  the  lens  parallel  to 
each  other. 

It  is,  therefore,  not  difficult  to  see  that,  if  the  object- 
point  were  placed  hetioeen  the  lens  and  its  principal  focus, 
the  rays  going  from  it  to  the  lens  would  be  divergent  still, 
after  leaving  the  lens,  though  less  divergent  than  before 
entering  it.  In  the  next  Exercise  we  shall  have  a  case  of 
this  kind. 

EXERCISE  27. 
VIRTUAL  IMAGE  FORMED  BY  A  LENS. 

Apparatus  :  The  same  as  for  the  previous  Exercise,  except  that 
the  sheet  of  paper  need  not  be  more  than  one  half  as  long,  and  that 


REFRACTION.  101 

the  arrow  upon  it  should  be  4  cm.  long  and  about  20  cm.  distant 
from  one  end. 

Place  the  lens  between  the  arrow  and  the  nearer  end  of  the 
sheet  of  paper,  at  a  distance  from  the  arrow  about  equal  to  f  its 
focal  length,  and  in  such  a  position  that  its  principal  axis  extends 
over  the  middle  point  of  the  arrow.  Place  the  small  block  (No. 
24)  with  vertical  pencil-mark  pointing  straight  down  at  the  middle 
point,  No.  3,  of  the  arrow.  Turn  the  vertical  part  of  the  wire  on 
the  other  block  so  that  it  will  point  up  instead  of  down,  and  place 
this  block  some  inches  behind  the  other  one. 

Holding  the  eye  8  or  10  inches  from  the  lens,  look  through  the 
lens  at  the  image  of  the  vertical  pencil-mark  and  at  the  same  time 
over  the  lens  at  the  verticad  patrt  of  the  wire.  Bring  the  'wire  into 
line  mth  the  image  and  then  by  the  usual  test  find  which  of  them 
is  the  more  distant.  Move  the  wire  back  and  forth  until  it  con- 
cides  in  position  with  the  image.  Then  mark  with  a  figure  3  the 
point  just  under  the  wire.  This  represents  the  image  of  oly'ect- 
point  No.  3. 

In  a  similar  manner  locate  the  images  of  points  1,  2,  4,  and  5. 

Connect  the  image-points  by  straight  Unes,  from  1  to  2,  from  2 
to  3,  etc.,  thus  forming  an  image  of  the  arrow. 

Draw  a  straight  line  from  each  image-point  to  its  corresponding 
object-point,  and  note  where  these  lines  will  cross  each  other  if 
continued. 

Suggestions  for  the  Lecture-room. 

The  images  observed  in  Exercise  27  were  virtual  images. 
They  could  not  be  shown  upon  a  screen,  and  were  not 
formed  by  the  actual  crossing  of  light  rays.  Fig.  88  will 
serve  to  illustrate  the  way  in  which  virtual  image-points 
are  formed. 

Let  AB  be  the  object,  placed  between  the  lens  LL'  and 
the  principal  focus  F'.  To  find  the  position  of  the  virtual 
image  of  the  point  A,  draw  AI  parallel  to  the  principal 
axis  of  the  lens.  This  ray  will,  after  leaving  the  lens,  pass 
through  F,  the  principal  focus  on  the  farther  side,  and  so 
will  appear  to  have  come  along  the  path  MF.  Draw  another 
ray,  A  C,  passing  through  the  centre  of  the  lens.    This  ray 


102 


PHYSICAL  EXPERIMENTS. 


will,  after  leaving  the  lens,  have  the  same  direction  as  before 
entering  it  and  will  be  represented  by  the  line  CN.  If,  then, 
we  carry  back  the  line  CN  till  it  crosses  the  line  MF,  also 
carried  backward,  the  point  A',  where  the  crossing  occurs, 
is  a  point  from  which  both  of  the  rays  appear  to  come.  A' 
is,  then,  the  virtual  image  of  A.  By  a  similar  process  B' 
is  found  to  be  the  virtual  image  of  B.  P' ,  the  image  of 
the  point  P,  is  here  represented  as  lying  in  the  straight 

•^^  A' 


I 
I 
I 

ip' 


L     r 


Fig.  88. 

line  between  A'  and  B' .    It  is  usually  so  represented  in 
books.     Exercise  27  shows  that  it  does  not  lie  there. 

The  image  A' B'  is  evidently  larger  then  the  object  AB. 
Whenever  a  virtual  image  is  formed  by  a  convex  lens,  this 
image  appears,  to  an  eye  placed  in  any  ordinary  position 
on  the  other  side  of  the  lens,  larger  than  the  real  object 
would  look  if  held  at  a  comfortable  seeing-distance  from 
the  eye.  Hence  the  name  magnifying-glass,  so  commonly 
given  to  a  lens  used  as  in  Fig.  88. 

We  have  seen  that  an  image  of  an  image  may  be  obtained 
with  mirrors.  So  the  image  formed  by  one  lens  may  be- 
come the  ohject  for  aiiother  lens. 

In  a  common  telescope  the  light  from  a  distant  object 
passes  first  through  a  lens,  or  combination  of  lenses,  called 


befbaction:  103 

the  objective,  and  forms  within  the  tube  of  the  telescope  a 
real  image  of  the  object.  Then  another  lens,  or  combina- 
tion of  lenses,  called  the  eye-2nece,  treats  this  image  just  as 
the  lens  LL'  in  Fig.  88  treats  the  object  AB. 

A  microscope,  like  a  telescope,  consists  of  an  objective 
and  an  eye-piece,  the  former  giving  a  real  image  which  the 
latter  treats  as  an  object.  The  objective  of  the  microscope 
is  of  very  short  focal  length,  and  the  object  to  be  examined 
is  placed  near  the  focus,  so  that  the  image  which  the  ob- 
jective forms  is  much  larger  than  the  object  itself.  The 
magnifying  process  thus  begun  is  continued  by  the  eye- 
piece. 


APPENDIX  A. 


All  the  articles  in  the  first  list  here  given,  except  No. 
31,  should  be  furnished  to  each  member  of  the  laboratory 
section.  Article  No.  31  should  be  furnished  to  each  pair 
of  experimenters. 

LIST  OF  ARTICLES  REFERRED  TO  BY  NUMBER 
IN  THE  "EXERCISES"  OF  THIS   BOOK. 

No.  1.     A  10-cm.  section  of  a  meter-rod. 

No.  2.  A  meter-rod  marked  on  one  side  in  feet  and 
inches. 

No.  3.  A  30-cm.  bevel-edged  measuring-stick,  marked 
on  one  side  in  inches. 

No.  4.  A  wooden  water-proofed  cylinder  about  8  cm. 
long  and  4.5  cm.  in  diameter,  loaded  internally  with  shot 
so  that  it  will  float  nearly  submerged  in  water. 

No,  5.  A  brass  can  about  14  cm.  tall  and  7  cm.  in  diam- 
eter, having  a  slightly  declining,  straight,  overflow  tube, 
about  6  cm.  long  and  0.8  cm.  in  internal  diameter,  extend- 
ing from  a  point  about  1.5  cm.,  clear,  below  the  top  of  the 
can  (see  Fig.  8). 

No.  6.  A  brass  catch-bucket,  with  a  wire  handle,  capa- 
ble of  holding  about  175  gm.  of  water,  and  weighing  not 
more  than  50  gm. 

No.  7.  An  8-oz.  spring- balance  graduated  to  0.5  oz. 
(The  Franklin  Educational  Company  of  Boston  offers  an 

105 


106  APPENDIX  A. 

improved  balance,  graduated  on  one  side  in  10-gm.  inter- 
vals and  on  the  other  side  in  0.25  oz.  intervals.    It  is, 


om 


iiifiiiiliDifiiiifmif 


Fio.  89. 

moreover,  especially  adapted  for  use  in  the  horizontal  posi- 
tion.    This  improved  balance  is  better  for  this  course.) 

Ho.  8.  A  rectangular  water-proofed  block  of  wood, 
about  7  cm.  long  and  4.5  cm.  square  on  the  end,  so  loaded 
internally  with  shot  that  it  will  sink  in  water,  but  not 
enough  to  make  it  weigh  more  than  225  gm. 

No.  9.  A  rectangular  water-proofed  cherry  block  about 
7.5  cm.  X  7.5  cm.  X  3.8  cm.  This  block  should  be 
smooth,  and  therefore  the  water-proofing  should  be  done 
by  soaking  it  in  very  hot  paraffin.  For  the  best  results 
this  soaking  should  be  done  in  a  vacuum.  Excess  of 
paraffin  should  be  scraped  off  before  the  block  is  used. 

No.  10.  A  one-gallon  glass  jar  of  good  quality.  (It  is 
poor  economy  to  buy  a  poor  jar  and  have  it  break  with  a 
liquid  in  it.) 

No.  11.  A  lump  of  roll  sulphur  weighing  about  175  or 
200  gm.  It  is  not  worth  while  to  cast  these  lumps  into 
regular  cylindrical  form. 

No.  12.  A  lead  sinker,  with  wire  handle,  weighing  about 
175  gm. 

No.  13.  A  water-proofed  wooden  cylinder  about  1  cm. 
in  diameter  and  20  cm.  long.  Doweling-rod,  furnished  by 
hardware  dealers,  serves  well  when  water-proofed. 

No.  14.  A  holder  for  keeping  No.  13  upright  in  water. 
It  consist  of  a  water-proofed  wooden  rod  about  12  cm.  long 
and  1.3  cm.  square  on  the  end,  provided  with  a  clasp  for 
attaching  it  to  the  side  of  a  jar,  and  with  two  screw-eyes 
projecting  from  one  side,  the  rings  of  which  are  large 


APPENDIX  A.  107 

enough  to  let  the  cylinder  Xo.  13  slip  easily  through  them, 
but  not  large  enough  to  allow  the  cylinder  to  tip  far  from 
the  vertical  position  (see  Fig.  18). 

No.  15.  A  cylindrical  glass  jar,  about  14  cm.  tall  and  10 
cm.  in  diameter,  with  level  top. 

No.  16.  A  broad-mouthed  bottle  with  ground -glass  stop- 
per, standing  not  much  more  than  11  cm.  tall  with  stopper, 
and  weighing,  when  filled  with  water,  about  175  or  200  gm. 

No.  17.  A  lever  and  supporting- bar.  The  lever  is  a  30- 
cm.  section  from  a  meter-rod,  pivoted  upon  the  smoothed 
cylindrical  body  of  a  brass  screw  which  is  driven  horizon- 
tally into  the  end  of  a  bar  of  hard  wood  about  25  cm.  long, 
5  cm.  wide,  and  3  cm.  thick.  A  brass  plate  projecting  from 
this  bar  and  overhanging  the  middle  of  the  lever  prevents 
the  lever  from  tipping  far,  while  it  allows  sufficient  freedom 
of  motion.  The  lever  itself,  except  for  a  distance  of  2  cm. 
each  side  of  the  middle,  is  cut  away  so  that  its  top  is  level 
with  the  upper  part  of  the  hole  through  the  centre.  There 
should  be  a  hole  about  0.5  cm.  in  diameter  running  down- 
ward through  the  middle  of  the  supporting-bar.    (Fig.  24.) 

No.  18  {A  and  B).  Two  brass  scale-pans  about  6.5  cm. 
square,  each  with  its  suspending  threads  weighing  accu- 
rately 1  oz.  (that  is,  not  differing  from  this  weight  by  more 
than  .01  oz.).  Each  pan  is  suspended  by  four  strong  linen 
threads  meeting  in  a  knot  about  20  cm.  above  the  pan,  two 
of  them  continuing  in  a  loop  about  4  cm.  long  above  this 
knot.     (Fig.  24.) 

No,  19.  A  set  of  iron  weights,  8  oz.,  4  oz.,  2  oz.,  and  two  1 
oz.,  making  a  total  of  16  oz.  No  weight  should  be  in 
error  more  than  ,01  oz. 

No.  20.  A  cubical  block  of  wood  about  3.7  cm.  on  each 
edge.  A  groove  about  1  cm.  wide  and  2  cm.  deep  extends 
through  the  lower  part  of  the  block  with  the  grain  of  the 
wood.  An  ordinary  short  screw  extends  through  one  side 
of  the  block  into  this  gi'oove,  and  serves  to  fix  the  block  in 


108  APPENDIX  A. 

position  upon  a  meter-rod.  Across  the  grain  at  the  top  of  the 
block  is  a  slot  about  0. 1  cm.  wide  and  0.5  cm.  deep.  (Fig.  83.) 

No.  21.  Two  bits  of  wood  each  about  8  cm.  long  and  1 
cm.  square  on  the  end,  for  supporting  the  spring-balance 
in  a  horizontal  position.     (Fig.  41.) 

No.  22.  A  plate-glass  mirror  about  15  cm.  long,  3.8  cm. 
wide,  and  0.2  cm.  thick,  the  coating  on  the  back  protected 
by  paint  or  varnish. 

No.  23  {A  and  B),  Two  straight-edged  rulers  of  some 
wood  that  will  keep  its  shape  well, — white  pine,  for  instance, 
— each  about  30  cm.  long,  5  cm.  wide,  and  1  cm.  thick. 

No.  24.  A  block  like  No.  20,  but  without  the  large  slot 
and  the  screw.  One  side  of  this  block  is  coated  with  white 
paper,  and  a  vertical  pencil-mark  or  ink-mark  is  made 
across  the  middle  of  this  paper.     (Fig.  86.) 

No.  25.  A  Walter  Smith  "  school  square,"  or  other 
equally  good  paper  protractor. 

No.  26.  A  cylindrical  mirror  of  nickel-plated  brass, 
about  4  cm.  tall  and  5  cm.  wide,  cut  from  seamless  tubing 
4  inches  in  diameter  and  y^  inch  thick,  mounted  upon  a 
semicircular  base-board  of  wood  of  the  proper  radius  of 
curvature.     The  base-board  should  be  about  1.5  cm.  thick. 

No.  27.  A  brass  partition  made  to  fit  the  small  glass  jar 
(No.  15),  and  to  extend  downward  into  the  jar  a  distance 
equal  to  about  one-third  the  diameter  of  the  jar.  It  should 
be  made  of  sheet  brass  about  .07  cm.  thick.    The  method 


□^ 


Fig.  90. 


of  shaping  and  adjusting  the  partition  is  suggested  by  Fig. 
90,  where  A  shows  a  side  view,  and  B  an  end  view,  of  the 
partition.    The  flanges  shown  in  B  are  bent  more  or  less 


APPEIWIX  A.  109 

in  adjusting  the  partition  to  fit  the  jar  closely,  but  without 
too  much  pressure. 

No.  28.  An  index  of  thin  sheet  brass  made  to  clasp  the 
side  of  the  jar  (Xo.  15).  This  index  is  a  strip  about  15  cm. 
long,  before  bending,  and  1  cm.  wide,  tapered  to  a  point  at 
one  end.  To  enable  it  to  clasp  the  jar,  about  3  cm.  at  the 
untapered  end  is  bent  over.     (See  ph  in  Fig.  75.) 

No.  29.  A  circular  (not  elliptical)  double-convex  spec- 
tacle-lens, having  a  focal  length  not  less  than  12  cm.  and 
not  more  than  16  cm.  This  lens  is  mounted  on  a  block 
similar  to  No.  20,  and  is  held  in  place  by  two  brass  strips, 
each  fastened  to  the  block  by  a  single  screw  and  extending 
about  3.5  cm.  above  the  top  of  the  block.  Each  strip  has 
a  narrow  vertical  slot,  cut  by  a  circular  saw,  which  does 
not  extend  to  the  top  of  the  strip.  The  edges  of  the  lens 
fit  into  these  slots,  and  the  lens  is  so  held  securely  in  an 
upright  position  (see  Fig.  83).  The  strips  may  be  about 
1  cm.  wide  and  .07  cm.  thick. 

No.  30.  A  white  cardboard  screen  about  8  cm.  square, 
of  such  thickness  as  to  be  held  firmly  in  the  narrow  slot  of 
the  small  block  No.  20.     (Fig.  83.)  ' 

No.  31.  A  small  kerosene  lamp  of  such  size  and  shape 
as  to  fit  it  for  the  use  shown  in  Fig.  84.  This  figure 
shows  the  lower  part  of  the  chimney  coated  with  asphaltum 
varnish,  which  is  scraped  off  in  one  cross-shaped  spot  on 
a  level  with  the  bright  part  of  the  flame.  A  far  better 
device  is  to  surround  the  lower  part  of  the  chimney  with  a 
thin  sheet  of  asbestos  paper,  having  a  hole  3  or  4  mm.  in 
diameter  at  the  height  of  the  flame.  The  lamp  must  be 
watched  to  see  that  the  flame  does  not  grow  too  tall. 

No.  32.  A  wire,  of  the  right  size  to  fit  into  the  narrow 
slot  of  No.  20,  bent  at  a  right  angle,  one  arm  about  6  cm. 
long,  the  other  about  4  cm.     (Fig.  86.) 


110 


APPENDIX  A. 


ARTICLES  USED  BY  THE  TEACHER,  BUT  NOT 
TO   BE  FURNISHED   TO   PUPILS. 

No.  I.  A  gauge  for  testing  pressure  at  various  points  and 
in  various  directions  in  a  jar  of  water.  In  Fig.  91,  w  is  a 
wooden  column  about  25  cm.  tall  and  1.5  cm.  square;  Z»  is  a 
brass  box,  with  brass  bottom  about  1.7  cm.  wide  and  1  cm. 
deep;  m  is  a  thin  rubber  membrane  fastened  across  the 


Fio.  91. 

mouth  of  this  box  by  means  of  sealing-wax — or,  better,  a 
cement  of  pitch  and  gutta-percha;  Ms  a  brass  tube  about 
8  cm.  long  and  0.5  cm.  in  outside  diameter;  ^j  and^;  are 
hard-rubber  pulleys  about  1.7  cm.  in  diameter  fitting  closely 
on  their  axes;  r  is  a  small  rubber  tube;  ^  is  a  glass  tube 


APPENDIX  A.  Ill 

passing  through  w;  *  is  a  short  cohimn  of  water  serving 
as  an  index.  In  use  a  band  of  strip-rubber,  such  as  toy- 
stores  supply,  connects  the  two  pulleys,  p  and  p,  so  that 
by  turning  the  axis  of  the  upper  pulley  between  the  thumb 
and  finger  the  gauge-face  m  may  be  turned  upward,  down- 
ward, or  sidewise  without  changing  level.  A  student-lamp 
chimney  with  stopper  for  one  end  accompanies  this  gauge. 

No.  II.  Apparatus  for  bursting  a  bottle  by  au  attempt 
to  compress  water  within  it. 

No.  III.  Glass  tube  about  1  m.  long,  closed  at  one  end, 
connected  by  a  strong  rubber  tube  25  cm.  long  with  an- 
other glass  tube  20  cm.  long.  (See  Fig.  10.  In  preparing 
this  apparatus  for  use  it  is  well  to  pour  in  mercury  until 
the  long  glass  tube  and  half  of  the  rubber  tube  are  filled.) 
A  suitable  support,  with  attached  meter-rod,  for  holding 
this  apparatus  when  used  as  a  barometer,  will  be  furnished 
with  it. 

No.  IV.  Strong  thistle-tube  (Fig.  11)  about  2.5  cm. 
wide,  covered  at  the  mouth  with  strong  sheet  rubber  and 
furnished  with  a  thick-walled  rubber  tube  about  20  cm. 
long. 

No.  V.  Small  air-pump  suitable  for  both  exhaustion 
and  compression. 

Only  one  experiment  with  the  air-pump  is  described  in 
this  book,  and  for  this  experiment  the  pump  alone,  without 
base  or  plate  for  bell- jars,  is  sufficient.  Manufacturers 
will  supply  a  base  and  plate  to  be  connected  with  the  pump 
proper  by  means  of  a  rubber  tube,  if  it  is  ordered. 

(With  this  air-pump  and  with  the  platform  balance,  No. 
XVII,  and  a  large  bottle,  one  may  perform  Exercise  XI  of 
Hall  &  Bergen's  Physics,  on  the  Specific  Gravity  of  Air.) 

No.  VI.  Bent  glass  tube  for  Boyle's  Law,  the  whole 
tube  about  1.5  m.  long  (Fig.  12). 

No.  VII.  Common  large  rubber  foot-ball,  with  a  rubber 
tube  about  30  cm.  long  attached  to  the  key  (Fig.  14). 


112  APPENDIX  A. 

No.  VIII.  Small  bottle  provided  with  rubber  stopper 
fitted  with  two  glass  tubes  as  in  Fig.  17. 

No.  IX.     Glass  model  of  lifting-pump  (Fig.  20). 

No.  X.     Glass  model  of  force-pump  (Fig.  21). 

No.  XI.     Hydrometer  for  liquids  less  dense  than  water. 

No.  XII.  Hydrometer  for  liquids  more  dense  than 
water. 

No.  Xm.  Glass  U-tube  (Fig.  22)  about  60  em.  long 
before  bending. 

No,  XIV.  Lead  Y-tube  with  attached  rubber  and  glass 
tubes,  and  two  small  tumblers  (Fig.  23). 

No.  XV.  Eight-inch  and  four-inch  wooden  disks  com- 
bined in  one  piece  for  use  as  a  pulley.  This  piece  is  fitted 
with  various  pins  (removable)  for  suspending  weights. 
It  is  mounted  much  like  the  lever  of  No.  17.  (See  Figs. 
26,  31,  32,  33,  and  37.) 

No.  XVI.  Centre-of-gravity  board,  with  suspension  and 
plummet  (Fig.  27). 

No.  XVII.  Platform  balance  weighing  from  1  kgm.  to 
0.1  gm.,  provided  with  a  set  of  brass  weights. 

No.  XVIII.  Well-made  small  brass  pulley  with  a  hook 
or  loop  (Fig.  39). 

No.  XIX.  Well-made  small  double  brass  pulley  with 
hook  or  loop  (Fig.  40). 

No.  XX.  An  inclined  plane  *  shown  about  one-fourth 
natural  size  in  Fig.  92.  The  roller  should  be  of  brass, 
accurately  turned.  It  weighs  with  its  frame  just  16  oz. 
The  graduations  of  the  scale  may  be  in  millimeters.  The 
apparatus  should  be  made  with  care. 

No.  XXI.  Pendulum-support  and  pendulum-balls  (Figs. 
50  and  51). 

No.  XXII.     Glass  prism  about  5  cm.  long. 

*  A  number  of  excellent  features  in  this  apparatus  are  due  to  Mr. 
Sweet  of  tlie  Rindge  Manual-Training  School  in  Cambridge. 


APPENDIX  A. 


113 


KTo.  XXIII.  Three  small  packages  of  dyestufFs  soluble 
in  water,  various  colors. 

No.  XXIV.  Three  glass  plates,  red,  green,  and  blue, 
about  10  cm.  square. 

No.  XXV.     Camera  obscura  consisting  of  two   paste- 


FiG.  98. 

board  tubes  each  about  25  cm.  long.  The  larger,  about 
5  cm.  in  diameter,  is  closed  at  one  end  save  at  the  centre, 
where  there  is  a  hole  about  0.1  cm.  in  diameter  in  a  thin 
partition.  The  smaller  tube,  about  4  cm.  in  diameter,  is 
closed  at  one  end  by  thin  tracing-paper.  (The  observer 
pushes  the  smaller  tube,  closed  end  foremost,  into  the 
larger  and  then,  pointing  the  apparatus  toward  a  window, 
looks  into  the  smaller  tube  and  moves  it  back  and  forth  in 
the  other  till  the  best  image  is  obtained.) 

No.  XXVI.     A  concave  spherical  mirror  12  or  15  cm.  in 
diameter. 


114  APPENDIX  A. 

MISCELLANEOUS  AETICLES. 

Two  pounds  of  clean  mercury. 

Two  pounds  of  assorted  soft  glass  tubing,  from  2  mm.  to 
8  mm.  inside  diameter. 

Six  feet  of  rubber  tubing,  about  5  mm.  inside,  that  will 
not  collapse  when  connected  with  the  air-pump. 

Piece  of  thin  sheet  rubber  about  G  inches  square,  for  use 
with  the  gauge,  No.  I. 

Set  of  cork-borers. 

Three-cornered  file  for  cutting  glass  tubing. 

Screw-driver. 

Pair  of  wire-cutting  pliers. 

One  half  pound  of  naked  copper  wire  of  the  same  size 
as  article  No.  32. 

Small  bottle  containing  a  few  ounces  of  mercury  and  an 
equal  volume  of  chloroform,  of  water,  and  of  kerosene  (see 
p.  34). 

COST  OF  APPARATUS. 

Three  firms  of  apparatus-makers,  which  in  alphabetical 
order  are 

The  Franklin  Educational  Company,  Hamilton  Place, 
Boston,  Mass., 

E.  S.  Ritchie  and  Sons  of  Brookline,  Mass., 

The  Ziegler  Electric  Company  (A.  P.  Gage  &  Sons),  141 
Franklin  St.,  Boston,  Mass., 
have  full  information   in  regard   to  the  apparatus  men- 
tioned in  these  lists,  and  will  undertake  to  supply  it. 

The  cost  of  a  single  set  of  the  pupil's  apparatus  as  de- 
scribed in  the  first  of  the  lists,  well  made  in  every  respect, 
will  be  not  far  from  five  dollars. 

The  cost  of  the  apparatus  in  the  second  list  and  of  tlie 
miscellaneous  articles  will  probably  be  in  the  neighborhood 
of  thirty  dollars. 


APPENDIX  A.  115 


LABOKATORY  TABLES. 

The  laboratory  tables  used  in  the  Cambridge  Grammar- 
schools  are  about  10  feet  long,  4  feet  wide,  and  2  feet  10 
inches  tall.  They  have  white-pine  tops  about  1^  inches 
thick,  and  heavy  white-wood  legs.  Extending  from  end 
to  end  over  each  table  are  two  horizontal  bars,  about  2 
inches  by  3  inches,  adjustable  at  various  heights  (which 
should  range  from  1^  feet  to  3^  feet  by  3-inch  intervals) 
above  the  table-top,  their  ends,  which  are  cut  in  tenons, 
sliding  in  grooves  in  the  supporting  posts.  These  posts 
are  fastened  to  the  frame  of  the  table  and  rise  through 
slots  in  the  table-top,  being  f,ush  with  the  ends  of  this  top 
and  about  10  inches  distant  from  the  sides.  Pins  of  iron 
or  wood  placed  in  holes  in  these  posts  support  the  ends  of 
the  horizontal  bars. 


APPENDIX  B. 


By  Frederick  8.  Cutter,  Master  of  the  Peabody  Grammar  School 
of  Cambridge,  Mass. 


The  course  of  study  for  the  grammar  schools  of  Cam- 
bridge by  a  revision  in  1892  was  shortened  and  enriched. 
In  shortening  the  course  the  work  of  six  years  was  so  ar- 
ranged that  pupils  could  complete  it  in  five  or  in  four 
years  without  omitting  or  repeating  any  part. 

In  the  enrichment  of  the  course  one  of  the  subjects 
added  was  elementary  physics,  by  the  laboratory  method, 
and  it  was  placed  in  the  ninth  or  highest  grade.  The  line 
of  work  to  be  pursued  was  laid  out  by  Prof.  Hall  of  Har- 
vard University. 

The  time  allotted  to  physics  was  one  hour  a  week 
throughout  the  year,  of  which  half  an  hour  was  for  labora- 
tory work  and  half  an  hour  for  recitation  in  the  class-room. 
For  the  work  in  the  laboratory  the  class  was  divided  into 
divisions  of  16  pupils  or  less.  While  one  division  was  at 
work  in  the  laboratory  under  an  assistant  teacher,  the 
other  pupils  of  the  class  were  reciting  or  studying  under 
the  direction  of  the  teacher  of  the  class-room.  Thus,  for 
a  class  of  48,  for  a  half-hour  lesson  in  the  laboratory,  the 
assistant  teacher  used  an  hour  and  a  half,  while  for  a  class 
of  56  or  60  two  hours  were  required.  In  my  own  school, 
in  which  the  class  numbered  60  pupils,  the  following  was 
the  pro-am : 

116 


APPENDIX  B. 


117 


Division. 

2-2.30. 

2.30-3. 

3-3.30. 

3.30-4. 

I 
II 

in 

IV 

Laboratory 
j  Geometry 
[  Geometry 

Study 

Geometry 
♦Laboratory 

Study 
*Geometry 

fReading 

Study 

Laboratory 
fReading 

Study 
j  Reading 
/  Reading 

Laboratory 

It  will  be  seen  that  during  each  of  the  four  periods  two 
divisions  together  were  taught  by  the  teacher  of  the  class- 
room, and  one  division  was  engaged  in  study.  Thus  the 
work  in  no  way  suffered  from  giving  the  laboratory  in- 
struction to  small  divisions.  The  half-hour  for  recitation 
was  taken  in  a  following  session  when  all  the  divisions 
were  taught  together  in  the  class-room  by  the  teacher  of 
physics. 

With  a  class  of  48  or  less  the  following  program  could 
be  used: 


Division. 

2-8.30. 

2.30-3. 

3-3.30. 

3.30-4. 

I 

n 
m 

Laboratory 

Geometry 

Study 

Study 

Laboratory 

Greometry 

Greometry 

Study 
Laboratory 

/     Physics 
I   recitation 

The  time  for  the  teaching  of  physics — and  also  geometry, 
which  has  been  introduced — was  obtained  in  the  revision 
of  the  program  by  completing  the  study  of  geography  in 
the  eighth  grade,  and  by  some  modifications  of  the  work 
in  arithmetic.  The  one  hour  a  week  for  physics  was  sup- 
plemented by  making  written  accounts  of  the  experiments 
a  part  of  the  language  work.  In  the  making  of  illustra- 
tions physics  was  further  correlated  with  the  work  in 
drawing. 

It  was  thought  at  first  by  some  persons  that  a  serious 


*  Recite  together. 


f  Recite  together. 


118  APPENDIX  B. 

objection  to  the  introduction  of  laboratory  physics  into 
grammar  schools,  with  their  large  classes,  would  be  the 
amount  of  time  and  labor  involved  on  the  part  of  the 
teacher  in  preparation  for,  and  in  clearing  up  after,  the 
laboratory  lessons.  But  I  have  found  that  the  teacher 
can  be  relieved  of  a  large  part  of  this  labor  by  pupilt: 
selected  from  the  class  who  will  gladly  serve  as  assist- 
ants. In  the  adjustment  of  the  apparatus  for  the  exper- 
iments nothing  should  be  done  for  the  pupils  that  they 
could  properly  be  expected  to  do  for  themselves.  But  in 
taking  from  the  cabinet,  caring  for,  and  putting  away,  the 
many  articles  used,  the  selected  pupils  can  render  valuable 
assistance.  Thus,  for  example,  one  of  my  boys  had  charge 
of  the  16  large  glass  jars, — the  filling  with  water,  the  empty- 
ing, and  the  putting  away  in  proper  condition.  Another 
pupil  had  the  care  of  the  16  spring-balances;  another,  the 
overflow-cans;  another,  suitable  strings  and  pins;  etc.  It 
was  the  duty  of  one  pupil  to  see  that  everything  needed 
for  an  experiment  was  finally  in  place,  that  there  might  be 
no  needless  loss  of  time  on  the  assembling  of  a  division. 
In  the  preparation  for  an  experiment  the  names  of  the 
articles  required  were  placed  upon  the  blackboard,  and  the 
pupils  having  charge  of  these  articles  would  see  that  they 
were  rightly  placed  in  the  few  moments  before  the  opening 
of  school,  so  that  little  or  no  time  for  this  purj)ose  would 
be  required  of  the  teacher.  At  the  close  of  school  the 
same  pupils  would  see  that  everything  was  clean  and  dry, 
and  put  away  in  its  proper  place.  The  plan  of  giving  to 
some  pupils  a  share  in  the  management  of  the  work 
served  to  increase  the  general  interest  and  to  promote 
success. 


INDEX. 


Accuracy  of  measurements,  3. 

Air,  compressibility  of,  23. 

Air-pinnp,  30. 

Angle  of  incidence,  75. 
of  reflection,  75. 
of  refraction,  87. 

Apparatus,    lists   of  and   manu- 
facturers of,  see  Appendix  A. 

Archimides,  principle  of,  15. 

Atmosphere,  pressure  of,  19. 

Barometer,  80. 

Boyle's  law,  22. 

Buoyant  force,  15. 

Camera  obscura,  79. 

Centre  of  gravity,  40. 

Centre  of  gravity  of  lever,  41. 

Chloroform,  34. 

Circle,  ratio  of  circumference  to 
diameter,  4. 

Color,  70. 

Conjugate  foci  of  lens,  95-97. 

Cost  of    apparatus    and    tables, 
see  Appendix  A. 

Cylindrical  mirror,  concave,  82. 
convex,  79. 

Daylight,  69. 

Density,  definition  of,  13. 

Distance,  measurement  of,  1. 

Equilibrium,  43. 

Error    of  measurement    and  of 
result,  5. 

Eye-piece,  103. 

Floating  body,  weight  of  water 
displaced  by,  18. 

Fluids,  definition  of,  21. 

Focal  length  of  lens,  93. 

Foot-ball,  air-pressure  within,  34. 


Force-pump,  33. 

Friction,  63,  64. 

Fulcrum  of  lever,  force  at,  47. 

Gases,  21. 

Gram,  definition  of,  relation  to 
ounce,  10. 

Gramniiir-schools,  physics  in, 
see  Intuoduction  and  Ap- 
pendix B. 

Hydrometers,  84. 

Hydrostatic  press,  25. 

Image,  real,  76. 

viitual,  or  apparent,  76. 

Image  of  an  image,  76. 

Inclined  plane,  57-63. 

Index  of  refraction,  87. 

Kaleidoscope,  78. 

Kerosene,  34. 

Lens,  91. 

Lever,  36. 

in  form  of  a  disk,  39. 
of  first  class,  43. 

Levers  of  second  and  third  classes, 
44,  45. 

Lifting-pump,  33. 

Light,  69. 

Liquids,  31. 

pressure  of,  16. 

Magnifying-glass,  103. 

Mariotte's  law,  22. 

Mercury,  34. 

Microscope,  103. 

Objective,  103. 

Parallel  forces,  rules  for  equi- 
librium of,  48. 

Parallelogram,  area  of,  7. 

Parallelogram  of  forces,  56. 

119 


120 


INDEX. 


Pascal's  experiments  on  atmos- 
pheric pressure,  19. 
Pendulum,  65-68. 
Plane  mirror,  images  in,  72. 
Plane  triangles,  area  of,  7. 
Power-arm  of  lever,  45. 
Pressure-gauge,  16. 
Principal  axis  of  lens,  92. 
Principal  focus  of  lens,  93. 
Prism,  69,  90. 
Pulleys,  49-52. 
Real  image  formed  by  a  lens, 

98-100. 
Reflection  of  light,  71. 
Refraction  of  light,  86. 
Right  triangle,  4. 
Secondary  axis  of  lens,  92. 
Siphon,  31. 

Solids,  definition  of,  21. 
Specific  gravity,  definition  of,  23. 

of  a  liquid,  32. 

of  a  solid  that  will  float  in 
water,  26,  29. 

of  a  solid  that  will  sink  in 
water,  23. 


Spectrum,  91. 

Spherical  mirror,  84. 

Spring-balance,  11  (note). 

testing  of,  12. 

Standards,  government,  3. 

Straight  line,  measurement  of,  2. 

Sulphate  of  copper,  70. 

solution,  32. 

Surface,  measurement  of,  5. 

Tables  for  laboratory,  see  Ap- 
pendix A. 

Telescope,  102. 

Three  forces  working   through 
one  point,  53. 

Torricelli's  experiment,  18. 

Transparent,  70. 

Units,  standard,  3. 

Virtual  image  formed  by  a  lens, 
100-102. 

Volume,  9. 

found  by  displacement  of 
water,  10. 

Wedge,  57. 

Weight,  two  meanings,  14. 

Weight-arm  of  lever,  4a.. 


Hall  and  Bergen's  Text-book  of  Physics. 

By  Edwin  H.  Hall,  Assistant  Professor  of  Physics  in  Harvard  College, 
and  Joseph  Y.  Bergen,  Jr.,  Junior  Master  in  the  English  High  School, 
Boston.     xviii  +  388pp.     izmo. 

This  book  contains  the  full  text  of  the  Harvard  College 
pamphlet  of  experiments,  interspersed  with  a  considerable 
number  of  minor  experiments  and  a  large  amount  of  discus- 
sion and  problem  work.  The  discussions  have  been  carefully 
planned  to  enable  the  student  to  derive  the  full  benefit  of  his 
experimental  work  and  to  guide  him  in  his  thinking ;  but  not 
to  relieve  him  of  the  necessity  of  thinking.  Accordingly, 
wherever  it  has  been  found  practicable,  the  conclusions  to  be 
drawn  from  an  experiment  have  been  withheld,  and  where 
they  have  to  be  made  the  basis  of  further  work  in  the  course, 
the  statement  of  them  has  been  deferred  somewhat  in  order 
that  the  student  may  have  opportunity  to  frame  one  for  him- 
self. The  problems,  which  are  very  numerous,  require  the 
pupil  to  apply  the  knowledge  he  has  gained  from  the  experi- 
ments, and  enable  the  teacher  to  ascertain  how  far  the  sub- 
ject-matter has  been  mastered. 

G.  W.  Krall,   Mamtal  Training] ^l&n  that  I  have  seen.     The  great 

School,  St.  Louis  : — Is  proving  very  trouble  of  works  of  this  kind  is  that 
satisfactory.  It  presents  the  true  they  tell  the  pupil  too  much.  This 
method  of  laboratory  work  in  Phy-  [  objection  is  largely  removed  in  Hall 
sics.  I  have  eighty  students  at!  &  Bergen's  book, 
work,  and  all  are  enjoying  the  ex-  J.  H.  Hutchinson,  Madison 
periments  and  taking  far  more  than  ( W/j.)  High  School: — Its  introduc- 
usual  interest.  '  tion  into  our  High  School  has  been 

A.  D.  Gray,  William  Penn  Char-  followed  by  excellent  results  thus 
ter  School,  Philadelphia  : — My  Phy-  far.  I  have  taught  Physics  for  some 
sics  class  had  already  begun  work  years,  but  never  with  so  much  satis- 
when  the  book  appeared,  but  the  faction  as  during  the  present  year, 
college  preparatory  division  changed  We  now  have  about  loo  using  the 
over  to  Hall  &  Bergen.  I  have  book,  and  most  of  them  are  very 
been  greatly  pleased  with  the  re-  much  interested, 
suits,  and  uniy  regret  that  I  have  F.  L.  Sevenoak,  Stevens  School, 
not  time  to  oversee  the  laboratory  Hoboken,  N.J.  : — We  adopted  some 
work  of  my  entire  class,  done  on  time  ago  as  our  method  of  teaching 
the  same  plan.  physics  the   plan  upon  which  Hall 

Arthur  O.  Norton,  Illinois  State  &  Bergen's  book  is  based.  No 
Normal  University : — I  find  it  more  other  plan  gives  such  satisfactory 
nearly  adapted  to  our  class  work' results.  I  am  glad  to  find  a  work 
than  any  other  work  on  the  same! so  exactly  suited  to  our  needs. 


Allen's  Laboratory  Exercises  in  Elementary  Physics. 

By  Charles  R.  Allen,  Instructor  in  the   New  Bedford,  Mass.,  High 
School.     Pupils'  Edition  .■  x  +  209  pp._  i2mo. 


Most  of  these  experiments  are  quantitative.  They  are 
planned  for  young  beginners,  do  not  employ  elaborate  and  ex- 
pensive apparatus,  require  no  more  than  forty-five  minutes 
each  in  the  laboratory,  and  are  so  framed  that  the  pupil  can 
prepare  himself  beforehand  to  make  the  most  of  his  time  there 
with  the  least  help  from  his  instructor.  There  are  six  exercises 
in  Magnetism,  eleven  in  Current  Electricity,  nine  in  Density 
and  Specific  Gravity,  thirteen  in  Heat,  twelve  in  Dynamics, 
four  in  Light,  and  two  in  Sound.  Sufficient  practice  in  methods 
of  mensuration  is  also  provided  for.  In  the  Teachers'  Edition 
67  pages  are  devoted  to  lists  of  apparatus  with  specifications 
for  construction,  suggestions  as  to  substitutes,  and  itemized 
estimates  of  cost,  together  with  detailed  hints  to  teachers  and 
references  to  standard  text-books. 


H.  B.  Davis,  Gushing  Academy, 
Ashburnham,  Mass.: — We  are  using 
this  year  Allen's  Laboratory  Man- 
ual. I  find  it  to  be  a  book  of  the 
highest  excellence.  Especially  is 
it  noteworthy  for  clearness  and 
conciseness,  two  of  the  most  desir- 
able qualities  in  a  laboratory  man- 
ual. With  this  book  in  his  hand 
the  pupil  knows  just  what  he  is 
seeking  after.  He  therefore  knows 
just  what  to  observe  and  what  not 
to  observe.  It  is  a  book  without 
equal  in  my  knowledge. 

Edward  Ellery,  Vermont  Acad- 
emy, Saxton's  River: — One  of  the 
most  prominent  features  of  the 
book,  which  recommended  it  to  us 
particularly,  is  the  plan  of  note- 
taking  it  suggests,  a  feature  which  I 
think  is  peculiar  to  this  book.  The 
experience  of  the  term  just  closed 
has  proved  to  our  satisfaction  that 
we  were  right  in  introducing  it. 
We  shall  continue  its  use. 


Arthur  O.  Norton,  Illinois  Slate 
Normal  University  : — It  is  unques- 
tionably the  best  arrangement  of 
quantitative  work  f(  r  beginners  that 
I  have  yet  seen.  Am  considering 
its  adoption.     [Adopted.] 

J.  C.  Packard,  Brookline  [Mass.] 
High  School: — At  last  we  have  a 
series  of  exercises  that  are  not  sup- 
plemented with  conclusions  and  a 
list  of  questions  that  do  not  "con- 
tain their  own  answers."  I  shall 
introduce  the  book. 

Geo.  L.  Chandler,  Newton 
(Mass.)  High  School: — It  seems  to 
be  an  excellent  book.  I  especially 
like  the  instructions  for  tabulating 
results.  Whatever  leads  to  system- 
atic arrangement  is  a  great  help. 

Chas.  h..yit.aA.,Dearborn- Morgan 
School.  Orange,  N.  J.: — I  am  much 
pleased  with  it.  The  appendixes 
contain  an  amount  of  information 
that  renders  them  invaluable  to  the 
teacher  of  physics. 


Barker's  Physics.    Advanced  Course. 

By  George    F.  Barker,  Professor  in  the   University  of   Pennsylvania. 
X  4-  go2  pp.     8vo.     {American  Science  Series.)     Revised. 

A  comprehensive  te)ft-book,  for  higher  college  classics, 
rigorous  in  method,  and  thoroughgoing  in  its  treatment  of  the 
subject  as  distinctively  the  science  of  energy.  After  a  general 
introductory  chapter,  the  subject  is  developed  under  three 
heads,  Mass-Physics,  Molecular  Physics,  and  Physics  of  Die 
.Ether.  Under  mass-physics,  energy  is  first  treated  of  as  a 
iiass-condition,  and  work  as  being  done  whenever  energy  is 
transferred  or  transformed.  The  properties  of  matter  are  next 
considered,  and  then  sound,  regarded  as  a  mass-vibration. 
Under  molecular  physics,  heat  alone  is  treated  and  as  a  mani- 
festation of  molecular  kinetic  energy.  Under  the  head  of 
aether-physics,  which  subject  occupies  three  fifths  of  the  vol- 
ume, are  grouped:  (i)  aether-vibration  or  radiation,  considered 
broadly  without  special  reference  to  light,  (2)  aether-stress  or 
electrostatics,  (3)  aether-vortices  or  magnetism,  and  (4)  aether- 
flow  or  electrokinetics. 

"  The  best  truly  modern  manual  of  physics  in  our  language" 
says  the  London  Chemical  News. 


Chas.  R.  Cross,  Professor  in 
Massachusetts  Institute  of  Tech- 
nology: — There  is  no  other  text- 
book that  seems  to  me  so  well 
adapted  for  high-grade  teaching  in 
general  physics,  and  I  shall  make 
use  of  it.   ( From  a  letter  to  the  author. ) 

Francis  H.  Smith,  Professor  in 
University  of  Virginia  : — The  work 
is  up  to  date  as  regards  facts.  It 
bears  the  marks  of  the  teacher  every- 
where, and  is  obviously  meant  for 
use  in  the  lecture-room.     It   shows 


Lucien  I.  Blake,  Professor  in 
University  of  Kansas  : — I  consider 
it  unqualifiedly  the  best  book  for 
college  work  on  modern  physics 
which  has  yet  appeared.  The  break- 
ing away  from  the  stereotyped 
methods,  the  absence  of  old  famil- 
iar cuts  and  descriptions  of  obso- 
lete apparatus,  is  refreshing ;  and 
Professor  Barker's  attempt  to  bring 
to  the  student  a  serious  work  based 
upon  the  best  recognized  modern 
research  is  singularly  successful. 


excellent  judgment  as  to  what  it  The  Nation : — The  work  de- 
leaves out.  It  is  judicious  in  its  I  serves  hearty  praise  for  its  fulness, 
scientific  perspeciive.  It  dignifies;  its  thoroughly  modern  spirit,  its 
the  science  by  making  principles  of  clearness,  and  a  certain  freshness 
more  importance  than  any  special  in  the  treatment  which  adds  to  its 
experiments,  while  it  by  no  means  real  value  as  well  as  to  its  attract- 
neglects  the  latter.  I  iveness. 


Woodhull's  First  Course  in  Science. 

By  John  F.  Woodhull,  Professor  in  the  Teachers'  College,  New  York 
City.     In  two  corafjanion-volumes. 
/.  Book  of  Experiments,     xiv+79  pp.     8vo. 

//.   Text-Book.    XV  +  133  pp.    i2mo.    doth. 

One  solution  of  the  problem  of  very  elementary  science 
teaching — a  solution  that  proceeds  on  the  intensive  rather  than 
the  extensive  basis.  These  lessons  make  ample  provision  for 
a  year's  work,  one  period  a  week;  they  are  entirely  within  the 
powers  of  average  pupils  ten  or  twelve  years  of  age.  All 
experiments  can  be  performed  on  the  pupil's  own  desk,  with- 
out darkening  the  room.  The  necessary  apparatus  costs  but 
$1.50  for  each  pupil,  and  most  of  it  is  in  the  nature  of  a  per- 
manent equipment. 

Light  has  been  chosen  as  the  subject  of  these  lessons  because 
it  exhibits  a  large  number  of  phenomena  at  once  capable  of 
easy  experimental  development,  and  having  numerous  useful 
daily  applications.  The  study  is  restricted  to  one  branch  of 
physics,  partly  to  inculcate  that  thoroughness  which  is  essen- 
tial to  true  science,  and  partly  for  the  sake  of  untrained  teach- 
ers, who  might  be  embarrassed  by  a  wider  range.  Most  of 
the  work  is  quantitative  in  character,  and  in  all  of  it  each  pupil 
must  proceed  independently  and  can  be  held  strictly  to  account. 
Each  experiment  illustrates  one  truth,  and  is  made  the  basis 
of  exercises  which  correlate  the  teachings  of  the  experiment 
with  the  pupil's  daily  experience  and  supply  problems  which 
connect  his  science  most  intimately  and  helpfully  with  his 
mathematics.  The  exercises  are  so  arranged  that  the  teacher 
can  make  the  necessary  adjustments  to  the  varying  degrees  of 
aptitude  in  his  pupils. 

The  material  of  each  lesson  is  separated  along  its  natural 
cleavage  into  that  which  gives  directions  and  asks  questions, 
and  that  which  formulates  results  and  contributes  additional 
information  when  the  pupil  is  in  a  position  to  desire  and 
appreciate  it.  These  divisions  are  put  into  the  two  mutually 
supplementary  volumes.  The  Book  of  Experiments  is  also 
a  note  book. 


Jackman's  Nature  Study  for  the  Common  Schools. 

By  Wilbur  S.  Jackman,  Teacher  of  Natural  Science,  Cook  County  Nor- 
mal School.  Chicago,   111.     x  4-448  pp.     i2mo. 

A  practicable  programme  of  lessons,  comprehending  the 
whole  circle  of  natural  objects  and  phenomena  with  which 
the  child  comes  in  contact.  His  equal  and  absorbing  interest 
in  every  detail  of  his  environment,  in  river,  cloud,  sunbeam, 
mountain,  physical  and  chemical  changes,  and  especially  in 
living  things  as  they  live,  is  brought  under  control  and  directed 
to  the  systematic  study  both  of  the  facts  and  their  relations. 
It  has  been  found  that  the  power  of  continuous  observation  is 
thus  cultivated  and  the  habit  of  trying  to  account  for  things 
established.  The  pupil  is  directed  through  each  topic  by  a 
series  of  questions  and  suggestions  which  he  is  to  use  in  exam- 
ining the  things  themselves,  sometimes  in  their  outdoor  sur- 
roundings, sometimes  by  means  of  class-room  experiments,  and 
he  is  made  regularly  to  record  the  results. 

Evanston(Ill.)  Course  of  Study:  i  of  the  science  knowledge  necessary 
— Jackman's  Nature  Study  is  the  by  actual  work;  also  that  science 
best  book  published  for  the  use  of  |  teaching  may  be  introduced  success- 
teachers.  It  is  full  of  valuable  sug-  j  fully  in  any  school  and  that  materials 
gestions  for  every  month  of  the  year 
in  the  several  divisions  of  natural 
science,  and  each  teacher  may  select 


therefrom  such  lessons  as  her  judg- 
ment dictates. 

C.  Henry  Kain,  /Iss'/  Sufi  Phil- 
addphia  {Pa.)  Public  Schools:—! 
most  enthusiastically  endorse  it.  It 
is  a  handbook  which  no  live  teacher 
can  afiford  to  dispense  with. 

W,  N.  Hailmann.  Suft  of  La 
Porte  {Ind.)  Schools  : — It  is  an  ex- 
cellent book  compiled  with  much 
love  for  children  and  for  the  subject 
of  instruction.  The  questions  which 
are  to  lead  to  observation  are  wisely 
selected  and  clearly  stated.  The 
book  offers  the  best  solution  I  have 
seen  of  the  problem  of  Nature  Study 
in  Elementary  Schools. 

New  York  School  Journal:— 
Teachers  will  find  by  examining  the 
book  that  it  is  possible  to  gain  much 


in  abundance  may  be  found  every- 
where. The  book  is  full  of  thought 
and  helpful  hints,  and  will  give  a 
great  impetus  to  the  study  of  science 
in  the  common  schools. 

George  H.  Martin,  Supervisor  of 
Ihe  Boston,  Afass.,  Public  Schools,  in 
School  and  College: — Each  set  of 
questions  is  preceded  by  a  few  practi- 
cal suggestions,  most  of  them  emi- 
nently wise  and  helpful.  It  is  in  these 
questions  that  the  teacher  will  find 
the  book  most  useful.  They  teach 
him  just  what  he  needs  to  know, — 
what  to  look  for  in  nature,  how  to 
read  the  "  manuscript  of  God." 
What  the  teacher  has  found  he  can 
lead  his  pupils  to  find,  and  by  read- 
ing the  books  to  which  the  author 
refers,  he  can  learn  the  scientific  re- 
lations of  his  facts,  and  can  answer 
the  questions  which  he  inspires. 


Black  and  Carter's  Natural  History  Lessons. 

By  George  Ashton  Black,  Ph.D..  and  Kathleen  Carter,  x  +  98 
pp.     i2mo. 

Part  I.  relates  to  the  objects  and  operations  that  have  en- 
grossed man  in  his  efforts  to  feed,  clothe,  and  house  himself. 
Part   II.    outlines   a  very  elementary  course   in    Botany  and 
Zoology. 
Bumpus's  Laboratory  Course  in  Invertebrate  Zoology. 

By  Hermon  C.  Bumpus,  Professor  in  Brown  University,  Instructor  at 
the  Marine  Biological  Laboratory,  Woods  Holl,  Mass.  Revised.  vi  -f 
157  pp.     i2mo. 

The  directions  cover  two  representatives  of  the  Protozoa,  seven 
of  the  Coelenterata,  three  of  the  Echinodermata,  four  of  the  Vermes, 
three  of  the  Mollusca,  seven  of  the  Crustacea,  two  of  the  Limulus 
and  Arachnoidea,  three  of  the  Atennata.  An  effort  has  been 
made  to  direct  the  work,  without,  at  the  same  time,  actually 
telling  the  student  all  that  there  is  to  be  learned  from  the 
specimen.  It  is  taken  for  granted  that  an  instructor  is  present 
to  assist  when  there  is  trouble,  and  to  demonstrate  many  things 
that  written  descriptions  might  only  render  more  confusing.  In 
the  Appendix  a  few  words  have  been  given  regarding  laboratory 
methods,  etc. 


M.  B.  Thomas,  Professor  in  Wa- 
bash College: — I  am  very  muchpleased 
with  it.  It  is  clearly  written  and 
does  not  tell  the  student  everything. 
So  many  manuals  leave  nothing  for 
the  student  to  find  out  for  himself. 

Albert  A.  Wright,  Professor  in 
Oberlin  College  : — It  is  admirable  in 
its  clearness  of  statement,  admirable 
in  what  it  omits.  It  brings  into  use 
a  number  of  easily  obtainable  types 
which  have  not  hitherto  been  treated 
of  in  laboratory  guides. 


Charles  W.  Dodge,  Professor  in 
University  of  Rochester  :  —  One  of 
the  most  valuable  features  of  the 
book  is  the  series  of  questions  which 
the  author  judiciously  uses  along 
with  statements  which  the  student  is 
expected  to  verify. 

George  Macloskie,  Professor  in 
Princeton  College  : — A  book  which  I 
like  very  much  and  hope  to  adopt 
next  September  as  text-book  for  a 
class  in  the  subject  which  it  covers. 


Cairns's  Manual  of  Quantitative  Chemical  Analysis. 

By  Frederick  A.  Cairns.  Revised  and  Edited  by  E.  Waller,  In- 
structor in  Analytical  Chemistry  in  School  of  Mines,  Columbia  College, 
viii  +  279  pp.    8vo. 

Hackel's  The  True  Grasses. 

Translated  from  "Die  naturlichen  Pflanzenfamilien "  by  F.  LAMSON- 
Scribner  and  Effie  A.  Southworth.    v  +  228  pp.    8vo. 


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